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Exponential stability estimate for derivative nonlinear Schrödinger equation Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-02-01 Xue Yang
We consider the derivative nonlinear Schrödinger equations iut=−uxx+V∗u+i∂x∂ūFu,ū,x∈Twith a nonlinearity F(u,ū) of order at least 3 at the origin. We prove that for almost all V, if the initial data is ɛ-small in the modified Sobolev space, the solution is stable over time intervals of order ɛ−1ɛ⋅ee1ɛ. Our findings extend the stability time elnɛɛ introduced by Cong (2022) to ee1ɛ.
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Limit cycle bifurcations in a class of piecewise Hamiltonian systems Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-02-01 Wenwen Hou, Maoan Han
In this paper, we first obtain explicit expressions of up to fourth order Melnikov functions for a class of piecewise Hamiltonian systems with two zones separated by two semi-straight lines. Then based on these expressions, we give upper bounds of the number of limit cycles bifurcated from a period annulus of a piecewise linear system under piecewise polynomial perturbations. The upper bounds are sharp
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Efficient detection of chaos through the computation of the Generalized Alignment Index (GALI) by the multi-particle method Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-02-01 Bertin Many Manda, Malcolm Hillebrand, Charalampos Skokos
We present a method for the computation of the Generalized Alignment Index (GALI), a fast and effective chaos indicator, using a multi-particle approach that avoids variational equations. We show that this approach is robust and accurate by deriving a leading-order error estimation for both the variational (VM) and the multi-particle (MPM) methods, which we validate by performing extensive numerical
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Practical fixed-time consensus for continuous action iterated dilemmas under communication and learning constraints Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-30 Hasnain Ali, Syed Muhammad Amrr
This paper introduces a continuous action iterated dilemma (CAID) model, enabling agents to adopt a spectrum of strategies beyond the traditional game theory practice of having only binary options. Existing research on the CAID problem often overlooks real-world challenges and assumes perfect communication and learning rates among agents. This work considers the limitations of complex networks, such
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Data-driven optimal prediction with control Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-29 Aleksandr Katrutsa, Ivan Oseledets, Sergey Utyuzhnikov
This study presents the extension of the data-driven optimal prediction approach to the dynamical system with control. The optimal prediction is used to analyze dynamical systems in which the states consist of resolved and unresolved variables. The latter variables cannot be measured explicitly. They may have smaller amplitudes and affect the resolved variables that can be measured. The optimal prediction
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Observer-based sliding mode boundary control of uncertain Markovian stochastic reaction–diffusion systems Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-28 Wei-Jie Zhou, Kai-Ning Wu, Yong-Xin Wu
This paper deals with the robust mean square exponential stabilization for uncertain Markovian stochastic reaction–diffusion systems (UMSRDS) via the observer-based sliding mode boundary control (SMBC). First, a suitable boundary-output-based observer is constructed for estimating the unknown system states. Next, to process the impact of Markovian switching, a mode-dependent integral sliding mode surface
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Hidden Markov Model for correlated Ornstein–Uhlenbeck observations and application to gasoline prices forecasting Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-27 Dimitrije Cicmilović
We propose a multivariate Ornstein–Uhlenbeck observation process governed by a Hidden Markov model, whereas the correlation between the observation processes is assumed. Optimal estimates of the model parameters are obtained by employing EM algorithm. The scope of application of the model are the gasoline prices in the US. We benchmark the dataset against the uncorrelated implementation of the Hidden
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Controllability analysis for impulsive multi-agent systems with switching effects Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-27 Qiyang Xiao, Yuhao Fang, Jiayuan Yan, Lei Shi, Ming-Feng Ge
Existing studies on multi-agent controllability are mainly developed based on the systems without state jumps, applicable solely to purely continuous or discrete cases. However, in some practical situations, state jumps, often termed impulsive effects, may occur during the evolution of agents. This paper deals with controllability for impulsive multi-agent systems (MASs) with switching characteristics
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The relationship between SBGK-LSE and NS-LSEs under continuum assumption Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-25 Lin Bi, Qiang Ma, He Gao, Jianxin Lv, Hao Wang, Xianxu Yuan
In the field of high-speed flight, the transition of the upper boundary layer of the aircraft has an significant impact on the aerodynamic characteristics and thermal protection of the aircraft. The classical Navier-Stokes (N–S) equations commonly have limitations because of the rarefied gas effect in the gas flow. The Boltzmann equation is based on the kinetic theory, which is suitable for the stability
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A type of efficient multigrid method for semilinear parabolic interface problems Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-25 Fan Chen, Ming Cui, Chenguang Zhou
This paper proposes and analyzes a type of efficient multigrid method, which is called multilevel correction method, for solving semilinear parabolic interface problems. The core idea of this method is that, at each time step, the semilinear elliptic interface problem’s solution is transformed into the same-scale linear elliptic interface problem’s solution in each level of multilevel space sequence
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Analysis of wave propagation and conservation laws for a shallow water model with two velocities via Lie symmetry Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-24 Aniruddha Kumar Sharma, Sumanta Shagolshem, Rajan Arora
This research investigates a one-dimensional system of quasi-linear hyperbolic partial differential equations, obtained by vertically averaging the Euler equations between artificial interfaces. This system represents a shallow water model with two velocities and is explored using Lie symmetry analysis to derive several closed-form solutions. Through symmetry analysis, a Lie group of transformations
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Remaining useful life prediction for stratospheric airships based on a channel and temporal attention network Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-24 Yuzhao Luo, Ming Zhu, Tian Chen, Zewei Zheng
Stratospheric airships are a research hotspot in the field of near space because of their durability, low cost, wide-area coverage, and relatively rapid response capabilities. Predicting the remaining useful life (RUL) of airships is the key to ensuring long-term stable residence and reducing maintenance and support costs. However, existing diagnostic and predictive techniques for airships primarily
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Use of fractional calculus to avoid divergence in Newton-like solver for solving one-dimensional nonlinear polynomial-based models Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-23 Sania Qureshi, Amanullah Soomro, Ioannis K. Argyros, Krzysztof Gdawiec, Ali Akgül, Marwan Alquran
There are many different fields of study where nonlinear polynomial-based models arise and need to be solved, making the study of root-finding iterative solvers an important topic of research. Our goal was to use the two most significant fractional differential operators, Caputo and Riemann–Liouville, and an existing time-efficient three-step Newton-like iterative solver to address the growing interest
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Modulated wave dynamics and excitation of rational breathers in positive ion–negative ion collisional plasmas Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-22 Debkumar Chakraborty, Biplab Maity, Samiran Ghosh
The rational breathers (Akhmediev, Kuznetsov-Ma, Peregrine) through the modulation instability (MI) are excited in positive ion - negative ion collisional plasmas by means of analytical and computation. The dynamics of the modulated waves are modeled by a nonlinear Schrödinger type equation with a linear damping term that arises due to the ion-ion weak collision. Both the low and high frequency waves
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On an age-structured model in moving boundaries: The effects of nonlocal diffusion and harvesting pulse Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-22 Haiyan Xu, Carlos Alberto Santos, Mengyun Zhang, Zhigui Lin
In order to understand how nonlocal diffusion and pulse intervention affect dynamics of species, we focus on an age-structured nonlocal diffusion model in moving and heterogeneous environment, where nonlocal diffusion describes the long range dispersal of species itself and time-periodic harvesting pulse exacting on the adult reflects human intervention. A generalized principal eigenvalue involving
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Modelling and vibration suppression of a transmission system with a curved beam-based nonlinear energy sink Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-22 Jinxin Dou, Zhenping Li, Muchuan Ding, Hongliang Yao, Tianzhi Yang
The electromagnetic excitation of the motor affects the vibration characteristics of the transmission system it drives. This study employs a curved beam-based nonlinear energy sink (CNES) as a suppression measure to reduce torsional vibrations in a multi-degree-of-freedom transmission system subjected to both electromagnetic and external excitations. An approximate expression for the electromagnetic
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Nonlinear dynamics analysis of labyrinth seal-rotor system considering internal friction in coupling Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-21 Yuan Wei, Jia Guo, Xiangyan Chen
The performance and efficiency of the mechanical system usually depend on the coordination between the rotor and other mechanical components. Due to the sliding motion between the coupling teeth, investigating the instability of the rotor is essential. The action of the coupling can cause changes in the seal performance. The article establishes a nonlinear dynamic rotor model that considers the coupling
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A novel spring-based nonlinear energy sink for torsional vibration suppression of long-shafting rotor system Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-21 Zhengqiu Xie, Kun Xie, Shuaishuai Ge, Zhigang Zhang, Ruizhi Shu, Rulong Tan, Wenbin Huang
In this paper, a novel spring-based nonlinear energy sink (SNES) is proposed for suppressing torsional vibrations in long-shaft rotor systems. The SNES functions by employing a piecewise linear stiffness, which is generated through the extrusion of springs. This mechanism provides the long-shaft rotor system with a restoring torque that can be characterized as a cubic nonlinear force. The paper details
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Distributed filtering for T-S fuzzy systems under cyber-attacks with time-varying saturation function Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-21 Yanping Qiu, Jun Cheng, Zhidong Zhou, Jinde Cao
This paper focuses on the distributed filter issue for a class of nonlinear systems under hybrid cyber-attacks, encompassing both deception attacks and denial of service (DoS) attacks with uncertain attack probabilities. In the sensor network, each filter estimates the output signals of the systems by dealing with the output measurements from the systems and the information received from its neighbors
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Adaptive decentralized control for second-order large-scale nonlinear systems via fully actuated system approach Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-21 Yifan Wang, Wei Sun
This study focuses on an adaptive decentralized control problem for second-order large-scale interconnected nonlinear systems with uncertainties. The proposed control method is the first study of second-order large-scale systems using fully actuated system approach, considering that most real physical systems are second-order, whereas the existing literature on large-scale systems primarily considers
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Unconditional superconvergence analysis of low-order conforming mixed finite element method for time-dependent incompressible MHD equations Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-20 Xiaochen Chu, Xiangyu Shi, Dongyang Shi
In this paper, we propose a backward Euler semi-implicit full discrete scheme for the time-dependent incompressible MHD equations and study the superconvergence behavior of the scheme. The spatial discretization is based on the bilinear-constant-bilinear elements for the velocity, pressure and magnetic fields, respectively, while the time discretization is based on the first-order backward Euler scheme
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Modified [formula omitted] Crank–Nicolson finite element methods with unconditional convergence for nonlinear time-fractional Schrödinger equations Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-20 Yan Wang, Baoli Yin, Yang Liu, Hong Li
The paper focuses on numerically solving the nonlinear time fractional Schrödinger equations. The modified L1 Crank–Nicolson scheme is used for the time discretization and the Galerkin finite element approximation is used in the spatial direction. Besides, we provide the proofs of stability by mathematical induction and unconditionally optimal error estimates by a discrete fractional Grönwall inequality
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Uniform position alignment estimate of a spherical flocking model with inter-particle bonding forces Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-20 Sun-Ho Choi, Dohyun Kwon, Hyowon Seo
We present a sufficient condition for asymptotic rendezvous of a Cucker-Smale type model on the unit sphere with an inter-particle bonding force. This second-order dynamical system includes a rotation operator defined on the surface of the three-dimensional unit sphere, and we derive an exponential decay estimate for the diameter of agent positions and demonstrate time-asymptotic flocking for a class
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On the number of normalized solutions for a fractional Schrödinger problem with logarithmic nonlinearity Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-20 Xiaolu Lin, Shenzhou Zheng
In this paper, we investigate the multiplicity and concentration of normalized solutions to a fractional logarithmic Schrödinger problem ɛ2s(−Δ)su+V(x)u=λu+ulogu2inRN with the prescribed mass ∫RN|u|2dx=aɛNwitha>0, where ɛ>0, λ∈R is unknown and appears as a Lagrange multiplier. By the minimization method combined with penalization technique and Ljusternik–Schnirelmann theory, we prove the multiplicity
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A new approach for efficient nonequilibrium quantum transport computation in electroluminescent quantum dots Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-19 Eunjung Lee, Uranchimeg Dorligjav, Richard James, Bowoon Kim, Hyung Uk Cho, Seungin Baek
The investigation of quantum dots, semiconductor structures renowned for their unique electronic and optical properties, has attracted considerable interest due to their diverse applications, spanning photovoltaics, optical communication, and quantum computing. However, the complex nature of multi-layered quantum dots, combined with their non-equilibrium behavior, presents a significant challenge in
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A nonlinear multivariate grey Bernoulli model for predicting innovation performance in high-tech industries Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-18 Sandang Guo, Jing Jia, Xu Han, Shuaishuai Geng
As China modernizes its industries, predicting innovation performance in high-tech industries is essential for crafting innovation-driven strategies. However, the system output of high-tech industries is influenced by multiple input factors with interaction effects, often exhibiting non-linearity and uncertainty. To address this, a novel nonlinear multivariate grey Bernoulli model considering interaction
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Solving optimal control problems of rigid-body dynamics with collisions using the hybrid minimum principle Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-18 Wei Hu, Jihao Long, Yaohua Zang, Weinan E, Jiequn Han
Collisions are common in many dynamical systems with real applications. They can be formulated as hybrid dynamical systems with discontinuities automatically triggered when states transverse certain manifolds. We present an algorithm for the optimal control problem of such hybrid dynamical systems based on solving the equations derived from the hybrid minimum principle (HMP). The algorithm is an iterative
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Stochastic stability of nonlinear mechanical metamaterial systems under combined Gaussian and Poisson white noises Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-18 Jiaojiao Sun, Zhiqiang Luo, Bo Yan
Mechanical metamaterials are a class of artificially designed structures usually modeled as high degree-of-freedom (DOF) systems. They, particularly nonlinear mechanical metamaterials, are widely applied in vibration suppression. This manuscript proposes a method to study the stochastic stability of nonlinear mechanical metamaterial systems under combined Gaussian and Poisson white noises. The mathematical
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Periodic perturbation of a 3D conservative flow with a heteroclinic connection to saddle-foci Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-18 A. Murillo, A. Vieiro
The 2-jet normal form of the elliptic volume-preserving Hopf-zero bifurcation provides a one-parameter family of volume-preserving vector fields with a pair of saddle-foci points whose 2-dimensional invariant manifolds form a 2-sphere of spiralling heteroclinic orbits. We study the effect of an external periodic forcing on the splitting of these 2-dimensional invariant manifolds. The internal frequency
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Umbrella Reinforcement Learning – computationally efficient tool for hard non-linear problems Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-17 Egor E. Nuzhin, Nikolay V. Brilliantov
We report a novel, computationally efficient approach for solving hard nonlinear problems of reinforcement learning (RL). Here we combine umbrella sampling, from computational physics/chemistry, with optimal control methods. The approach is realized on the basis of neural networks, with the use of policy gradient. It outperforms, by computational efficiency and implementation universality, all available
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Qualitative study for the system of waste plastic management in the ocean: A discrete-time deterministic model Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-17 Mahmood Parsamanesh, Mehmet Gümüş
Ocean waste is a serious environmental problem affecting marine ecosystems and marine life. A large portion of this waste consists of recyclable materials. If managed correctly, it provides both economic and environmental benefits. By using mathematical models, it is possible to predict the spread of these wastes and develop strategies. In this paper, a discrete-time compartmental model is introduced
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Nonlinear dynamics effect of viscosity of cytosol into the microtubules and exact solutions Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-17 Tabapsi Kamdem Rostand, Belobo Belobo Didier, Bansi Kamdem Christel Delphin, Dang Koko Adamou, Tabi Conrad Bertrand, Kofané Timoléon Crépin
The viscosity of the cytosol plays a crucial role in the biology of microtubules (MTs), affecting their architecture and dynamics function. Understanding the overall functionality of this parameter is essential. The effect of viscosity on MT dynamics is studied when modelling longitudinal and angular displacements. The rotating wave approximation is used to derive two uncoupled complex Ginzburg–Landau
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New LKF approach for non-weighted [formula omitted] gain of switched linear systems with delay Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-17 Yachun Yang, Xiaodi Li, Xinsong Yang
This paper focuses on observer-state feedback control for global asymptotic stabilization (GAS) with non-weighted L2-gain of switched linear systems with delay. Two kinds of mode-pendent event-triggered control (ETCs) are proposed for both the observer and the controller: one can exclude the Zeno phenomenon and adjust the event intervals by tuning the parameters while the other cannot. An innovative
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Expansion of magnetic fluid around a convex corner into vacuum Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-17 Fei Zhu
In this paper, we study the expansion of Noble-Abel gas into the vacuum around a convex corner for the two-dimensional compressible magnetohydrodynamic system. Unlike previous studies, we study the incoming flow at sound speed, a discontinuous boundary value problem for a two-dimensional set of magnetohydrodynamic equations. When u0=w0, the technical difficulty of the O point being a singularity arises
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Stochastic resonance and dynamic event-triggered impulsive control of a variable-order fractional information diffusion system with hybrid noise Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-17 Ying Jing, Youguo Wang, Qiqing Zhai
The processes and control of information diffusion have received significant attention in the information age. Considering the prevalent environmental noise and individual memory, this paper constructs a variable-order fractional information diffusion model on heterogeneous networks, incorporating internal Gaussian white noise and external Lévy noise. Since the introduction of noise leading to stochastic
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Regularity estimations of the 2D/3D unsteady incompressible Darcy–Brinkman equations with double-diffusive convection and their finite element analysis based on incremental pressure correction method Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-16 Linlin Jiang, Demin Liu
In this paper, the 2D/3D unsteady incompressible Darcy–Brinkman equations with double-diffusive convection are considered. Firstly, several a priori regularity estimates of the weak solutions are derived, and then two fully decoupled incremental pressure correction finite element methods (IPC FEMs) are proposed, i.e., the first-order and second-order standard IPC (SIPC) methods. Based on the above
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Existence of traveling pulses for a diffusive prey–predator model with strong Allee effect and weak distributed delay Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-16 Yuhang Wu, Mingkang Ni
In this article, we investigate the existence of traveling pulses in a diffusive prey–predator model with a strong Allee effect and weak distributed delay. Assuming that the growth and death rates of the predator are much smaller than those of the prey and that the average delay is small, we transform the model into a singularly perturbed problem with a three-time scale structure. Using generalized
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The primary resonance of a Duffing oscillator with a restoring force of fractional-order derivatives by the extended Galerkin method Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-15 Chencheng Lian, Baochen Meng, Huimin Jing, Hui Chen, Fang Xie, Ji Wang
The nonlinear vibrations have wide appearances in many scientific and engineering problems to be solved by various techniques to satisfy requirements for solutions. With many different equations of nonlinear features, approximate methods have been suggested and tested to enable simple, accurate, and efficient solution procedures in dealing with increasingly complex problems. The introduction of fractional-order
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Command-filter based predefined-time neural adaptive decentralized control for interconnected systems with dynamic uncertainties Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-15 Zhucheng Liu, Feisheng Yang, Heng Li
This article studies the predefined-time controller construction problem for non-strict feedback nonlinear large-scale interconnected systems including unmodeled dynamics and dynamic disturbances. The uncertain nonlinearities and interconnections in the studied systems are universally approximated by neural networks. The observable dynamic signals created by the constructed auxiliary systems are utilized
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Some practical regards on the application of the physics-informed sparse identification for strongly NESs Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-14 Qinghua Liu, Zehao Hou, Ying Zhang, Xiaojun Xu, Dong Jiang
Strongly Nonlinear Energy Sink structures (NESs) have been widely developed to achieve better performance of vibration suppression recently. Utilizing nonlinear stiffness designs poses great challenges to the system's restoring force measurement and parameter identification. The SINDy (sparse identification of nonlinear dynamics) method has significantly enhanced the efficacy of parameter identification
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Effects of pulse amplitude modulation on relaxation oscillations in the Duffing system Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-14 Jin Song, Mengke Wei, Wenjie Zuo, Xiujing Han, Qinsheng Bi
This paper reports on the fast-slow dynamics induced by pulse amplitude modulation (PAM). Typically, PAM transmits information signals by altering the amplitude of the pulse signal, with the core concept being that the amplitude of the pulse sequence varies according to the input data. It was observed that introducing additional pulse excitation in the Duffing system results in a relaxation oscillation
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Weak and Wasserstein convergence of periodic measures of stochastic neural field lattice models with Heaviside ’s operators and locally Lipschitz Lévy noises Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-13 Hailang Bai, Mingkai Yuan, Dexin Li, Yunshun Wu
We study the global-in-time well-posedness and periodic measures for a class neural field lattice models (with Heaviside’s operators) defined on the high-dimensional integer set Zd, and driven by locally Lipschitz Lévy noises. We first formulate the stochastic neural field lattice equations into abstract stochastic systems defined in the infinite-dimensional weighted Hilbert space, and then prove the
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A closed-form solution for pricing European-style options under the Heston model with credit and liquidity risks Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-12 Xin-Jiang He, Shou-De Huang, Sha Lin
Credit risks are one type of hazardous financial risks, which results in the necessity of considering vulnerable options. Two involved assets, corresponding to underlying and option seller’s ones, both follow Heston stochastic volatility with different parameters, and their prices are discounted via a stochastic factor relying on stochastic market-wide liquidity. We then develop a general formula after
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On a matrix KdV6 equation Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-12 Pilar R. Gordoa, Andrew Pickering, Jonathan A.D. Wattis
The so-called KdV6 equation has, since its discovery, been the subject of much interest. In this paper we present a matrix version of this equation. On the one hand, we use the Darboux transformation to derive its Bäcklund transformation and a nonlinear superposition formula. These are then used, in the case of upper-triangular matrices, to obtain one- and two-soliton solutions. We find that wave components
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The neural network basis method for nonlinear partial differential equations and its Gauss–Newton optimizer Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-11 Jianguo Huang, Haohao Wu
This paper focuses on designing the neural network basis method (NNBM) and its optimizer for solving systems of nonlinear partial differential equations (PDEs) in two/three dimensions. We first discretize the underlying problem in terms of a set of neural network basis functions from ELM-type methods combined with the collocation method, so as to produce a nonlinear least squares method (which is named
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Finite-time stability of stochastic systems with proportional delay involving hybrid impulses Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-10 Haofeng Xu, Quanxin Zhu
In this article, the stochastic finite-time stability of impulsive stochastic nonlinear systems involving proportional delay is investigated via the Lyapunov-Razumikhin method and the stochastic analysis technique. It is worth noting that both destabilizing impulses and stabilizing impulses are considered, i.e., the obtained results are based on the combination of impulsive control and impulsive disturbance
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A novel distributed neural FTC strategy for interconnected nonlinear systems with unknown higher powers and its applications to CIPs Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-10 Jiyu Zhu, Qikun Shen
This article focuses on the distributed fault-tolerant control (FTC) problem for a class of interconnected nonlinear systems with unknown higher powers. In order to reduce the excessive resource consumption and address the denial-of-service (DoS) attacks, an event-triggered communication mechanism (ECM) with multiple DoS detectors is developed for interconnected nonlinear systems for the first time
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Eigenfunction expansion method to characterize Rayleigh waves in nonlocal orthotropic thermoelastic medium with double porosity Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-10 Chandra Sekhar Mahato, Siddhartha Biswas
The present manuscript addresses the Rayleigh wave propagation in a nonlocal orthotropic thermoelastic half-space with double porosity within the dual-phase-lag model of hyperbolic thermoelasticity. An eigenvalue technique is used to solve the resulting vector-matrix differential equation. Boundary conditions include stress-free, thermally insulated, and isothermal surfaces. The frequency equations
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Robust globally divergence-free weak Galerkin methods for unsteady incompressible convective Brinkman–Forchheimer equations Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-10 Xiaojuan Wang, Jihong Xiao, Xiaoping Xie, Shiquan Zhang
This paper develops and analyzes a class of semi-discrete and fully discrete weak Galerkin finite element methods for unsteady incompressible convective Brinkman–Forchheimer equations. For the spatial discretization, the methods adopt the piecewise polynomials of degrees m(m≥1) and m−1 respectively to approximate the velocity and pressure inside the elements, and piecewise polynomials of degree m to
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On global stability of nonlinear systems with unbounded and distributed delays and a dominating non-delay term Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-09 Elena Braverman, Cemil Tunç, Osman Tunç
A system with, generally, unbounded and non-continuous delays is considered as a perturbation of a linear non-delay system. Boundedness of solutions, stability, global asymptotic stability, uniform exponential stability are established with a variety of methods, including designing a Lyapunov–Krasovskii functional and integral transformations. The system incorporates a linear non-delay part and a sum
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Homogenization for stochastic complex Ginzburg–Landau equation on the half-line with rapid Neumann boundary fluctuation Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-07 Yangyang Shi, Hongjun Gao
In the current study, we explore the homogenization of the stochastic complex Ginzburg–Landau equation on the half-line with rapid Neumann boundary fluctuation. Precisely, we first establish the local and global existence and uniqueness of the mild solution within the space L∞([0,T];H1(R+)). Subsequently, we discuss the tightness of the mild solution in C([0,T];H1(R+)) under suitable conditions. Ultimately
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Multiscale grayscale dispersion entropy: A new nonlinear dynamics metric for time series analysis Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-07 Yuxing Li, Yilan Lou, Chunli Zhang
Link dispersion entropy (LDE), as an improvement of dispersion entropy (DE), focuses on transition states between adjacent dispersion patterns. However, the transition states of dispersion patterns at different intervals are ignored and parameters of LDE have a significant impact on entropy value. To address these problems, grayscale dispersion entropy (GDE) is proposed, which introduces transition
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Global dynamics of delayed discrete-time SEIR negative information propagation model with multi-platform and cross-transmission mechanism Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-07 Yutao Yan, Shuzhen Yu, Zhiyong Yu, Haijun Jiang, Hui Wang
Taking into account the phenomenon of cross-platform propagation of network information and multi-platform network environments, this paper constructs two discrete-time negative information propagation models with time delays. For the single platform model, we first prove that the information-free equilibrium (IFE) is locally asymptotically stable (LA-stable) and globally asymptotically stable (GA-stable)
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Oscillatory wave bifurcation and spatiotemporal patterns in fractional subhyperbolic reaction-diffusion systems Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-07 Bohdan Datsko, Vasyl Gafiychuk
The stability of a two-component time-fractional reaction-diffusion system during its linear stage is analyzed, revealing the emergence of a new type of instability at specific values of the fractional derivative order. With this instability, perturbations with finite wave numbers become unstable and cause spatially inhomogeneous oscillations. A comprehensive spectral study identified such type of
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The asymptotic problem on contact Hamilton–Jacobi equations with state constraints Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-06 Xiaotian Hu
We investigate the long time behavior of the viscosity solution for the evolutionary contact Hamilton–Jacobi equation with state constraints. Our analysis reveals that the viscosity solution uniformly converges to a viscosity solution of the corresponding stationary contact Hamilton–Jacobi equation with state constraints as time goes to infinity.
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Data-driven discovery of conservation laws from trajectories via neural deflation Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-04 Shaoxuan Chen, Panayotis G. Kevrekidis, Hong-Kun Zhang, Wei Zhu
In an earlier work by a subset of the present authors W. Zhu et al. (2023), the method of the so-called neural deflation was introduced towards identifying a complete set of functionally independent conservation laws of a nonlinear dynamical system. Here, we extend by a significant step this proposal. Instead of using the explicit knowledge of the underlying equations of motion, we develop the method
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Nonlinear stochastic vibration of GPRMF cylindrical shell with harmonic and white noise excitations Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-04 Liyuan Wang, Dongxu Cao, Jiayang Gu
This study focuses on analyzing the behavior of a graphene platelet reinforced metal foams (GPRMF) cylindrical shell under both harmonic and random excitation using advanced stochastic methods. A nonlinear stochastic differential equation describes the shell's random vibration, and the probability density function (PDF) of the vibration response is calculated using the random integral approach. The
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A parallel full domain partition method for Stokes and Navier–Stokes type variational inequalities with damping Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-03 Bo Zheng, Yueqiang Shang
Motivated by reducing the computational time and computer storage requirements in the numerical simulations, we present a parallel full domain partition method based on finite element approximations for Stokes and Navier–Stokes type variational inequalities with damping in this paper. Within this parallel method, each subproblem used to calculate an approximate solution is actually a global problem
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A novel computational approach to reconstructing evolutionary fitness in self-replicating systems Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-03 Oleg Kuzenkov, Andrew Yu. Morozov, Ivan Bataev
Evolutionary fitness is a fundamental concept, widely utilised in modelling natural selection in self-replicating systems. This concept describes selective advantages of inherited elements in the underlying system. Maximisation of evolutionary fitness is traditionally used to predict the outcome of long-term evolution, in particular, to provide the best behavioural strategy or life-history trait. Deriving
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Practical fixed-time Lyapunov criterion of stochastic nonlinear systems and its application Commun. Nonlinear Sci. Numer. Simul. (IF 3.4) Pub Date : 2025-01-03 Jingjing You, Abudujelil Abudurahman, Shuxin Liu
This article investigates the practical fixed-time stability in probability (PFxT-SP) of stochastic nonlinear systems (SNS). First, a unified PFxT-SP criterion is developed by using the stochastic differential equation theory and Lyapunov functional method. Building on this foundation, several specific judgment forms of the PFxT-SP are established and corresponding estimates for the settling times