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Optimal long time error estimates of a second-order decoupled finite element method for the Stokes–Darcy problem Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-04-15 Liming Guo
In this paper, we propose a second-order decoupled finite element method based on lagging a part of the interfacial coupling terms for the time dependent Stokes–Darcy problem, which only need to solve two sub-physical problems sequentially. Under a modest time step restriction (physical parameters), the optimal long time error estimates are obtained both in the norm and in the norm. Numerical results
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Numerical analysis of age-structured HIV model with general transmission mechanism Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-04-15 Zhuzan Wang, Zhanwen Yang, Guoqiu Yang, Chiping Zhang
In this paper, we discuss the numerical representation of the linearly implicit Euler method for an age-structured HIV infection model with a general transmission mechanism. We first define the basic reproduction number of the continuous model, and present the stability results of the equilibriums. For the numerical process, we establish the solvability of the system and the non-negativity and convergence
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Finite-time stability of Caputo fractional fuzzy differential equations with delay in granular sense Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-04-15 Feixiang Yan, Danfeng Luo
This manuscript focuses on investigating a class of Caputo fractional fuzzy differential system with time delay. Firstly, we understand the granular form of fuzzy numbers from a novel perspective, which contains more information than the usual membership function. Subsequently, using a successive approximation approach under the granular arithmetic context, we demonstrate the existence of the solution
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Superconvergence error analysis of linearized semi-implicit bilinear-constant SAV finite element method for the time-dependent Navier–Stokes equations Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-04-12 Huaijun Yang, Dongyang Shi
In this paper, based on the scalar auxiliary variable (SAV) approach, the superconvergence error analysis is investigated for the time-dependent Navier–Stokes equations. In which, an equivalent system of the Navier–Stokes equations with three variables and a fully-discrete scheme is developed with semi-implicit Euler discretization for the temporal direction and low-order bilinear-constant finite element
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Unconditional stability and error estimates of the modified characteristics FEMs for the Micropolar Navier–Stokes Equations Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-04-12 Zhiyong Si, Yao Ji, Yunxia Wang
In this paper, the unconditional stability and optimal error estimate of the velocity, pressure and angular velocity for the modified characteristics FEMs of the unsteady Micropolar Naiver–Stokes Equations (MNSE) are presented. In this method, the nonlinear equation is linearized by the characteristic finite element method for dealing with the time derivative term and the convection term. Basing on
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One- and two-level Arrow–Hurwicz-type iterative algorithms for the stationary Smagorinsky model Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-04-12 Dan Lai, Pengzhan Huang, Yinnian He
In this article, based on finite element discretization, we propose one- and two-level Arrow–Hurwicz-type iterative algorithms for solving the steady-state Smagorinsky equations. The two-level Arrow–Hurwicz-type iterative algorithm involves solving a linearization Smagorinsky problem by the Arrow–Hurwicz-type iteration on a coarse mesh with mesh size and one Oseen-type linear problem on a fine mesh
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Energy dissipation laws of time filtered BDF methods up to fourth-order for the molecular beam epitaxial equation Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-04-10 Jiexin Wang, Yuanyuan Kang, Hong-lin Liao
This report presents the time filtered BDF- (FiBDF-) methods up to fourth-order time accuracy for the molecular beam epitaxial equation with no-slope selection. The new -order methods are developed by introducing an inexpensive post-filtering step to the variable-step BDF- methods. We show that the FiBDF- methods are uniquely solvable and volume conservative. Some novel discrete gradient structures
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Analysis of bifurcation and chaotic behavior of the micro piezoelectric pipe-line robot drive system with stick - slip mechanism Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-04-10 Jichun Xing, Chao Ning, Yuan Zhi, Ian Howard
Pipeline robots using the conventional driving mode have encountered a bottleneck in miniaturization. To address this problem, a micro piezoelectric pipeline robot based on the inertia stick-slip driving principle is proposed in this paper. The robot is well suited to the inspection needs of micro pipes. However, undesirable design parameters found during the structural optimization phase can lead
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Planar quartic–quadratic fold–fold singularity of Filippov systems and its bifurcation Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-04-08 Tiago Carvalho
In this paper it is exhibited the bifurcation scenario concerning a typical singularity of planar piecewise smooth vector fields in two zones. This singularity is characterized by a quadratic contact of one vector field and a quartic contact of another vector field at the same point of the switching manifold. By means of a three parameter perturbation, we observe the presence of bifurcations like:
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A Crank–Nicolson leap-frog scheme for the unsteady incompressible magnetohydrodynamics equations Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-04-06 Zhiyong Si, Mingyi Wang, Yunxia Wang
This paper presents a Crank–Nicolson leap-frog (CNLF) scheme for the unsteady incompressible magnetohydrodynamics (MHD) equations. The spatial discretization adopts the Galerkin finite element method (FEM), and the temporal discretization employs the CNLF method for linear terms and the semi-implicit method for nonlinear terms. The first step uses Stokes style’s scheme, the second step employs the
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Finite element method for a generalized constant delay diffusion equation Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-04-06 Weiping Bu, Sizhu Guan, Xiaohong Xu, Yifa Tang
This paper considers the finite element method to solve a generalized constant delay diffusion equation. The regularity of the solution of the considered model is investigated, which is the first time to discover that the solution has non-uniform multi-singularity in time compared with Tan et al. (2022). To overcome the multi-singularity, a symmetrical graded mesh is used to devise the fully discrete
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On the convergence of linear and nonlinear Parareal methods for the Cahn–Hilliard equation Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-04-04 Gobinda Garai, Bankim C. Mandal
This paper introduces, analyses, and implements efficient time parallel methods for solving the Cahn–Hilliard (CH) equation. Efficient numerical methods for the CH equation are crucial due to its wide range of applications. In particular, simulating the CH equation often requires long computational times to obtain the solution during the phase coarsening stage. Therefore, there is a need to accelerate
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Rao-Blackwellized particle smoothing for mixed linear/nonlinear state-space model with asynchronously dependent noise processes Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-04-04 Yunqi Chen, Zhibin Yan, Xing Zhang
For the mixed linear/nonlinear state-space model (ML/NLSSM) with asynchronously dependent noise processes (ADNP), this paper aims at designing Rao-Blackwellized particle smoothing (RBPS) algorithms via the sequential Monte Carlo sampling method to solve its fixed-interval smoothing problem. Asynchronous dependency leads to the current measurement depending not only on the current state, but also on
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Dynamics and scaling of internally cooled convection Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-04-04 Lokahith Agasthya, Caroline Jane Muller
Our goal is to investigate fundamental properties of the system of internally cooled convection. The system consists of an upward thermal flux at the lower boundary, a mean temperature lapse-rate and a constant cooling term in the bulk with the bulk cooling in thermal equilibrium with the input heat flux. This simple model represents idealised dry convection in the atmospheric boundary layer, where
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Fuzzy fractional delay differential inclusions driven by hemivariational inequalities in Banach spaces Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-04-04 Danfeng Wu, Minghao Chen
This paper investigates a novel class of nonlinear dynamical fuzzy systems referred to as fuzzy fractional delay differential hemivariational inequalities (FFDDHVIs) in Banach spaces. These systems integrate fractional fuzzy differential inclusions with delay and hemivariational inequalities. The existence theorem for the HVIs is established based on the KKM theorem. Moreover, specific propositions
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Corrigendum to “article: A stochastic theta-SEIHRD model: adding randomness to covid-19 spread,” [Communications in Nonlinear Science and Numerical Simulation, 115 (2022), 106731] Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-04-04 Álvaro Leitao-Rodríguez, Carlos Vázquez
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A [formula omitted]-power neurodynamic approach to distributed nonconvex optimization Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-30 Yangxia Li, Zicong Xia, Yang Liu, Jinde Cao, Mahmoud Abdel-Aty
In this paper, a neurodynamic optimization approach based on a -power transformation Lagrangian function is developed for distributed nonconvex optimization. A new Lagrangian function is proposed to eliminate dual gaps of nonconvex problems, and a distributed average tracking approach is developed for estimating global objective function value. Based on the Lagrangian function and the distributed average
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Optimal harvest for predator–prey fishery models with variable price and marine protected area Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-28 Cheng Chu, Wenjun Liu, Guangying Lv, Ali Moussaoui, Pierre Auger
In this paper, we propose a predator–prey fishery model with prey harvesting, variable price and marine protected area. We assume the price changes faster than other processes such as population growth and predation, and get a slow fast Ordinary Differential Equation (ODE) system. A simplified three-dimensional model is obtained by using approximate aggregation methods. The results show that there
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Analysis and simulation of an integro-differential Lotka–Volterra model with variable reproduction rates and optimal control Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-27 Anderson L.A. de Araujo, Artur C. Fassoni, Kamila F.L. Madalena, Luís F. Salvino
In this work, we present an integro-differential system that generalizes the classical Lotka–Volterra model of competition. The model considers population heterogeneity with respect to reproduction rates, local diffusion in the aspect space and control interventions. We perform a rigorous mathematical analysis proving results on existence and uniqueness of solutions and on existence of optimal controls
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Global sensitivity analysis of plasma instabilities via active subspaces Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-24 Soraya Terrab, Stephen Pankavich
Active subspace analysis is a useful computational tool to identify and exploit the most important linear combinations in the space of a model’s input parameters. These directions depend inherently on a quantity of interest, which can be represented as a function from input parameters to model outputs. As the dynamics of many plasma models are driven by potentially uncertain parameter values, the utilization
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Existence conditions for bifurcations of homoclinic orbits in a railway wheelset model Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-24 Xingang Wang, Hongjun Cao
This paper investigates the bifurcations of homoclinic orbits to hyperbolic saddle points in a simplified railway wheelset model with cubic and quintuple nonlinear terms. Using Melnikov’s method, the sufficient conditions for the existence of the supercritical and the subcritical pitchfork bifurcations of homoclinic orbits are proven. To determine the integrability of the variational equations around
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Sequential time scaling transformation technique for time-delay optimal control problem Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-23 Yin Chen, Xi Zhu, Changjun Yu, Kok Lay Teo
The time-scaling transformation technique used within the computational framework of control parameterization serves as an effective method for the optimization of control switching time as well as the control value for time-delay optimal control problems. However, the conventional time-scaling transformation stipulates that the switching times for all control components must be identical, which may
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On an asymmetric functional-coefficient ARCH-M model Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-22 Xiaotong Zhong, Qiang Xiong
This paper proposes an asymmetric functional-coefficient autoregressive conditional heteroscedasticity in mean (ARCH-M) model, which allows for asymmetry in the volatility. The profile likelihood approach is applied to estimate the parametric and nonparametric components. Under some regularity assumptions, we derive asymptotic behavior of the proposed estimator. To avoid model misspecification, the
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Mathematical modeling and dynamic analysis for cancer resistance incorporating persister cells Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-21 Ke Qi, Shun Wang, Yuyang Xiao, Xiufen Zou
Drug resistance is a key impediment to cancer treatment, however, the resistance mechanism remains controversial. Experiment evidence indicated that persister cells, a subpopulation in a transient pseudo-dormant state, are posited to play a potential role in the emergence of resistance. In this study, we propose a novel mathematical model for describing the interactions among sensitive, persister,
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Fractional diamagnetic Kepler problem and elastic collisions Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-21 Eduardo Scafi, Marcus Werner Beims
In this work, we consider an application of fractional derivatives to realistic physical situations, namely the elastic collision of particles and the nonintegrable diamagnetic Kepler problem. The origin of fractional dynamics can be nonlocal interacting dynamics, memory effects, environments with fractal interacting properties, and relaxation processes, among others. In the case of collisions, considering
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Error estimates of a space–time Legendre spectral method for solving the Korteweg–de Vries equation Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-21 Lin Sang, Hua Wu
In this paper, a space–time spectral method for solving the Korteweg–de Vries equation is considered. The discrete schemes of the method are based on the Legendre–Petrov–Galerkin method in spatial direction and the Legendre-tau method in temporal direction with nonperiodic boundary conditions. Stability analysis results and error estimates are obtained in -norm by introducing a cut-off function without
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No two without three: Modeling dynamics of the trio RNA virus-defective interfering genomes-satellite RNAs Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-20 J. Tomás Lázaro, Ariadna Albó, Tomás Alarcón, Santiago F. Elena, Josep Sardanyés
Almost all viruses, regardless of their genomic material, produce defective viral genomes (DVG) as an unavoidable byproduct of their error-prone replication. Defective interfering (DI) elements are a subgroup of DVGs that have been shown to interfere with the replication of the wild-type (WT) virus. Along with DIs, other genetic elements known as satellite RNAs (satRNAs), that show no genetic relatedness
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Correlation and collective behaviour in Adler-type locally coupled oscillators at the edge of chaos Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-19 E. Estevez-Rams, K. Garcia-Medina, B. Aragón-Fernández
Dynamical systems can be analysed as computational devices capable of performing information processing. In coupled oscillators, enlarged capabilities are expected when the set of units is formed by subsets with collective behaviour within them but weak correlation between the subsets. A system of non-linear oscillators weakly coupled in the phase approximation is studied. The informational distance
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Projective synchronization for distinct fractional-order neural networks consist of inconsistent orders via sliding mode control Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-16 Junshuang Zhou, Deyi Li, Guici Chen, Shiping Wen
The present study delves into the projective synchronization for distinct fractional-order neural networks consist of inconsistent orders, employing the principles of sliding mode control and incorporating fractional operators within the controller. Firstly, incorporating the fractional-order derivative into the controller facilitates the derivation of a synchronous error system, and a well-suited
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Fuzzy adaptive event-triggered synchronization control mechanism for T–S fuzzy RDNNs under deception attacks Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-16 Shuoting Wang, Kaibo Shi, Jinde Cao, Shiping Wen
In this paper, a fuzzy-dependent adaptive event-triggered mechanism (FAETM) for synchronizing Takagi–Sugeno (T–S) fuzzy reaction–diffusion neural networks (RDNNs) is developed while considering deception attacks. Firstly, a general neural network model considering both fuzzy logic rules and reaction–diffusion terms is established. Secondly, a FAETM based on an aperiodic sampling period is presented
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Lyapunov stability of fuzzy dynamical systems based on fuzzy-number-valued function granular differentiability Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-16 Hong Yang, Yu Chen
Lyapunov stability theory provides a powerful technique for stability analysis of dynamical systems, particularly for the stability of nonlinear dynamical system. This paper deals with the stability of fuzzy dynamical systems using a novel notion called granular fuzzy Lyapunov function. In order to analyze the stability, some new notions are introduced such as fuzzy equilibrium point, the ball of fuzzy
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Leader-following synchronization for Lur’e networks via dynamic event-triggered control Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-16 Zhengxin Wang, Haonan Xu, Sijiao Sun, Yang Liu, Min Xiao, Jinde Cao
This paper considers synchronization of Lur’e systems under a dynamic event-triggered framework. To facilitate the study, a novel time-varying sampled-data-related dynamic event-triggered control (ETC) related to fully discrete local information is proposed, which does not require continuous communication among nodes and naturally avoids Zeno behavior. By using the Halanay inequality, a number of sufficient
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Novel superconvergence analysis of a low order FEM for nonlinear time-fractional Joule heating problem Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-16 Xiangyu Shi, Haijie Wang, Dongyang Shi
The aim of this paper is to develop and investigate a fully-discrete scheme with conforming element for the nonlinear time-fractional Joule heating problem in which the Caputo derivative is approximated by the classical method. First, a novel superclose estimate in the -norm is derived rigorously with some new analysis techniques under low regularity of the solutions rather than and required in the
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A two-strain avian–human influenza model with environmental transmission: Stability analysis and optimal control strategies Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-15 Calvin Tadmon, Arnaud Feukouo Fossi, Berge Tsanou
On the basis of the WHO legitimated fear that there will be an avian influenza virus strain capable of mutating once it reaches the human population and sustains human-to-human transmissions, we formulate an hypothetical mathematical model which accounts for the environmental transmission and mutation of an avian influenza virus having the ability to spill over into the human population and become
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Non-smooth dynamics of a fishery model with a two-threshold harvesting policy Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-15 Joydeb Bhattacharyya, Malay Banerjee, Soumitro Banerjee
The non-linear dynamical systems theory helps implement regulatory measures to control the growth and evolution of various populations. While invasion by alien fish species is an emerging threat to native fish species in marine ecosystems, a suitable fishery management protocol needs to be incorporated in marine protected areas (MPAs) to mitigate the problem. We propose a policy of selective harvesting
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Global exponential synchronization of switching neural networks with leakage time-varying delays Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-15 Shilei Yuan, Yantao Wang, Xian Zhang
In this paper, the synchronization problem of a class of switching neural networks with leakage time-varying delays is studied. A system solution-based direct analysis method is proposed to derive the sufficient conditions of global exponential synchronization for master–slave systems. Firstly, the state variable expression of the error system is derived by constructing a suitable regulation function
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Symmetry of the stochastic Rayleigh equation and features of bubble dynamics near the Blake threshold Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-15 A.O. Maksimov
Ultrasonic cleaning is widely accepted as being an extremely efficient method of decontaminating a diverse range of objects and products. Optimization of the process is generally achieved by variation in the intensity and the spectrum of ultrasound. This spectrum takes the form of individual lines, which are superimposed on the noise background. The stochastic dynamics of the bubble in the acoustic
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A relaxation approach to modeling properties of hyperbolic–parabolic type models Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-12 Eduardo Abreu, Arthur Espírito Santo, Wanderson Lambert, John Pérez
In this work, we propose a novel relaxation modeling approach for partial differential equations (PDEs) involving convective and diffusive terms. We reformulate the original convection–diffusion problem as a system of hyperbolic equations coupled with relaxation terms. In contrast to existing literature on relaxation modeling, where the solution of the reformulated problem converges to certain types
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Stability of periodic waves for the defocusing fractional cubic nonlinear Schrödinger equation Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-12 Handan Borluk, Gulcin M. Muslu, Fábio Natali
In this paper, we determine the spectral instability of periodic odd waves for the defocusing fractional cubic nonlinear Schrödinger equation. Our approach is based on periodic perturbations that have the same period as the standing wave solution, and we construct real periodic waves by minimizing a suitable constrained problem. The odd solution generates three negative simple eigenvalues for the associated
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Modulation instability and collision dynamics of solitons in birefringence optical fibers Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-11 Fei-Fei Liu, Xing Lü, Jian-Ping Wang, Xian-Wei Zhou
In this paper, we investigate soliton modulation instability and collision dynamics in the birefringence optical fibers. Soliton transmission in the picosecond or femtosecond range in optical fibers is described by the coupled hybrid nonlinear Schrödinger equations. We focus on the modulation instability of the plane wave solutions and the gain spectrum under different parameters. The three-soliton
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Enhanced parallel computation for time-fractional fluid dynamics: A fast time-stepping method with Newton-Krylov-Schwarz solver Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-11 Li Xia, Xiaoyun Jiang, Fanhai Zeng, Zeng Lin, Shanlin Qin, Rongliang Chen
This paper presents a sum-of-exponentials domain decomposition method for the numerical simulation of two-dimensional unsteady fluid flow and heat transfer using a time-fractional fluid model. We employ a fast time-stepping approach to discretize the time-fractional derivatives, followed by the application of a parallel Newton-Krylov-Schwarz algorithm to solve the resulting discrete nonlinear system
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Folding Domain Functions (FDF): A Random Variable Transformation technique for the non-invertible case, with applications to RDEs Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-11 Fabrizio Masullo, Fabio Zanolin, Josep Bonet Avalos
The Random Variable Transformation (RVT) method is a fundamental tool for determining the probability distribution function associated with a Random Variable (RV) where is a RV and is a suitable transformation. In the usual applications of this method, one has to evaluate the derivative of This can be a straightforward procedure when is invertible, while difficulties may arise when is non-invertible
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Analysis of quasi-variational–hemivariational inequalities with applications to Bingham-type fluids Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-11 Stanisław Migórski, Yang Chao, Jiahong He, Sylwia Dudek
In this paper we study the sensitivity analysis of elliptic quasi-variational–hemivariational inequalities with constraint. The upper semicontinuity property of the solution map with respect to a parameter is established. An application to the steady-state incompressible Navier–Stokes equation with mixed boundary conditions in a model for a generalized Newtonian fluid of Bingham-type is provided. The
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Stability and nonlinear vibrations of an inclined axially moving beam considering self-weight Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-11 Zhenhao Shi, Chao Wang, Guo Yao
The transmission device of the astronautic exploration vehicle can be regarded as an inclined beam experiencing axial motion under varying gravitational acceleration and tilt angle. Understanding the instability and vibration characteristics of this structure with axial movement is crucial for the dynamic design of the astronautic exploration vehicle. This paper discusses the stability and non-linear
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Fractional damping induces resonant behavior in the Duffing oscillator Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-11 Mattia Coccolo, Jesús M. Seoane, Miguel A.F. Sanjuán
The interaction between the fractional order parameter and the damping parameter can play a relevant role for introducing different dynamical behaviors in a physical system. Here, we study the Duffing oscillator with a fractional damping term. Our findings show that for certain values of the fractional order parameter, the damping parameter, and the forcing amplitude high oscillations amplitude can
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Shape transformation on curved surfaces using a phase-field model Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-11 Hyundong Kim, Seungyoon Kang, Gyeonggyu Lee, Sungha Yoon, Junseok Kim
Shape transformation on evolving curved surfaces is essential for its diverse applications across various scientific disciplines and facilitates the deeper understanding of natural phenomena, the development of new materials, and engineering design optimization. In this study, we develop a phase-field model and its numerical methods for shape transformation on curved surfaces. A modified surface Allen–Cahn
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The virtual element method with interior penalty for the fourth-order singular perturbation problem Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-08 Bei Zhang, Jikun Zhao
We present the virtual element method with interior penalty to solve a fourth-order singular perturbation problem. In order to estimate the nonconformity error, the degrees of freedom on edges are changed to the moments of functions in the interior penalty scheme. To do this, we design a special -type projection that can be uniquely determined by the new degrees of freedom. With the help of the -type
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A structure-preserving projection method with formal second-order accuracy for the incompressible Navier–Stokes equations Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-07 Junxiang Yang, Yibao Li, Junseok Kim
The incompressible Navier–Stokes equations play an important role in describing extensive fluid phenomena in science and engineering. With some specific boundary treatments, the Navier–Stokes equations can satisfy an energy evolutional structure with respect to kinetic energy and works done by external forces. If the external forces are absent, the energy dissipation law is obtained. This work aims
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The dimension reduction method of two-grid Crank–Nicolson mixed finite element solution coefficient vectors for nonlinear fourth-order reaction diffusion equation with temporal fractional derivative Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-07 Yihui Zeng, Yuejie Li, Yitian Zeng, Yihua Cai, Zhendong Luo
Herein, we mainly resort to a proper orthogonal decomposition (POD) to study the dimension reduction of unknown solution coefficient vectors in the two-grid Crank–Nicolson mixed finite element (CNMFE) (TGCNMFE) method for the nonlinear fourth-order reaction diffusion equation with temporal fractional derivative and establish a new reduced-dimension extrapolated TGCNMFE (RDETGCNMFE) method. For this
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Security synchronization problem for stochastic complex networks via event-triggered impulsive control with actuation delays Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-07 Zhengli Liu, Mengzhuo Luo, Jun Cheng, Iyad Katib, Kaibo Shi
This study focused on the security synchronization problem for stochastic complex networks (SCNs) via event-triggered impulsive control (ETIC) with actuation delays. Firstly, incorporating the network topology and the Lyapunov function theory, a novel event-triggered mechanism (ETM) is devised, which accounts for actuation delays; Secondly, an ETM-based quantizer is introduced to optimize network resources
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Novel passivity and dissipativity criteria for discrete-time fractional generalized delayed Cohen–Grossberg neural networks Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-06 Chen Wang, Hai Zhang, Danli Wen, Mouquan Shen, Liwei Li, Zhihao Zhang
This paper pays attention to the passivity and dissipativity for discrete-time fractional generalized delayed Cohen-Grossberg neural networks. A new fractional passive lemma is firstly proposed for discrete-time system by means of the Lyapunov functional. This facilitates the discussion of system stabilization in terms of input and output energy. Some passive and dissipative conditions are established
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Mechanism and quantitative criterion of free vibration characteristics of hydraulic systems using the water hammer reflection coefficient Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-06 Yi Liu, Jian Zhang, Xiaodong Yu, WeiXin Qiu, Zhe Liu
Hydraulic vibration is a periodic hydraulic transient in piping systems, which can result in local damage and operating accidents involving hydraulic, mechanical, and electrical systems. However, traditional hydraulic vibration theory is limited in practical application because of its complex mathematical form and low computational efficiency. This study presents a free vibration analysis method of
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Numerical analysis of the kinetic equation describing isotropic 4-wave interactions in non-linear physical systems Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-06 B.V. Semisalov, S.B. Medvedev, S.V. Nazarenko, M.P. Fedoruk
We develop a numerical method for solving kinetic equations (KEs) that describe out-of-equilibrium isotropic nonlinear four-wave interactions in optics, deep-water wave theory, physics of superfluids and Bose gases, and in other applications. High complexity of studying numerically the wave kinetics in these applications is related with the multi-scale nature of turbulence and with power-law behaviour
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Hedging lookback-barrier option by Malliavin calculus in a mixed fractional Brownian motion environment Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-06 Kefan Liu, Jichao Zhang, Yueting Yang
We present a Malliavin calculus approach to a mixed fractional Brownian motion option hedging model, that adequately describes, e.g., the hedging of a lookback-barrier option with the floating strike price. The Markovian setup and smooth stochastic differentials are necessary components in the payoff function for classical -hedging of a contingent claim. This is in contrast to the Malliavin calculus
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Breather solutions for a radially symmetric curl-curl wave equation with double power nonlinearity Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-06 Xin Meng, Shuguan Ji
This paper is concerned with breather solutions of a radially symmetric curl-curl wave equation with double power nonlinearity where , is the unknown function, and are radially symmetric coefficient functions with . By considering the solutions with a special form , we obtain a family of ordinary differential equations (ODEs) parameterized by the radial variable . Then we characterize periodic behaviors
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Numerical study of distributed-order Bessel fractional derivative with application to Euler–Poisson–Darboux equation Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-05 Hadiseh Jafari Arimi, Mostafa Eslami, Alireza Ansari
The present paper introduces the distributed-order (DO) Bessel fractional derivative for study of the Euler–Poisson–Darboux (EPD) equation including the spatial Riesz fractional derivative (RFD). For this purpose, we discretize the integral term of the DO fractional derivative and approximate the RFD derivative. We thereafter apply an implicit difference method (IDM) for numerical analysis and solvability
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Group consensus for fractional-order heterogeneous multi-agent systems under cooperation-competition networks with time delays Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-05 Fenglan Sun, Yunpeng Han, Wei Zhu, Jürgen Kurths
The issue of group consensus for heterogeneous fractional-order multi-agent systems under the cooperation-competition networks with time delays is investigated in this paper. Novel group consensus control protocols with input and communication delays are designed based on cooperative-competitive interaction. The considered multi-agent systems consists of fractional order dynamics with the single integrator
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Sensitivity and unpredictability in semiflows on topological spaces Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-05 Arpit Mahajan, Rahul Thakur, Ruchi Das
We introduce and study notions of topological sensitivity and topologically unpredictable point for semiflows on topological spaces. Both these notions are related with their original versions. With the help of topological transitivity, we provide some sufficient conditions for a semiflow to be topologically sensitive. The notion of topologically unpredictable point is studied on the arbitrary product
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Stability for Markov switching stochastic delay systems binding event-triggered mechanism to activate multi-impulse jumps Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-04 Zhenyue Wang, Quanxin Zhu
This paper focuses on the th moment exponentially stability for Markov switching and multi-impulse jumps stochastic time-varying delay system, where the switching behavior among subsystems of the target system is determined by Markov chains, and the occurrence of impulsive jumps is decided according to event-triggered impulsive mechanism when certain well-designed conditions are satisfied. By applying
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Hybrid event-triggered control for networked switched Takagi–Sugeno fuzzy systems with aperiodic DoS attacks Commun. Nonlinear Sci. Numer. Simul. (IF 3.9) Pub Date : 2024-03-01 Siyi Guo, Yuechao Ma
This article investigates the event-triggered control problem for networked switched Takagi–Sugeno fuzzy systems (NSTSFSs) with denial of service (DoS) attacks. First, an attack-instant-constrained hybrid event-triggered mechanism (ETM) is proposed, which uses the acknowledgment character (ACK) detection scheme. It can describe the triggering schemes under different attack intervals and modify the