This research scrutinizes the issue of finite-time extended dissipativity-based sliding mode control design for large-scale interconnected partial differential equation (PDE) systems under the influence of external disturbances, input time-varying delays and cyber-attacks. In particular, the interconnection among the large-scale PDEs is governed by a nonlinear coupling protocol. Primarily, to prioritize

This work is devoted to deriving the Onsager–Machlup function for a class of degenerate stochastic dynamical systems with (non-Gaussian) Lévy noise as well as Brownian noise. This is obtained based on the Girsanov transformation and then by a path representation. Moreover, this Onsager–Machlup function may be regarded as a Lagrangian giving the most probable transition pathways. The Hamilton–Pontryagin

In this paper, a novel H∞ fuzzy control criterion with variable convergence rate is proposed for T-S fuzzy impulsive dynamical systems (T-SFIDSs). Unlike the traditional H∞ fuzzy control criterion, the criterion introduced in this paper not only ensures the stability and a certain degree of immunity of the system, but also controls the convergence rate of the system states. Firstly, the concept of

Hypergraph dismantling aims to identify the smallest set of nodes whose removal disrupts the hypergraph, breaking it into subextensive connected components. However, many existing dismantling approaches either overlook higher-order interactions commonly present in real-world systems or give limited consideration to the role of community structures in the dismantling process. To address these limitations

This paper proposes a new geometric fault detection and isolation (FDI) strategy for Markov jump nonlinear systems with uncertain transition probabilities and mode-dependent time-varying delays. Firstly, the unobservability subspace is defined for each mode of Markov jump nonlinear system, and further constructed by designing the finite-step convergence algorithm. Secondly, utilizing the geometric

This work focuses on the development of a mathematical model of the thermal protection system, in which the fractional Caputo derivative is used for the first time in one of the layers of the model. So far, no studies have been identified that consider a model of this kind. The introduction of fractional derivatives is justified by the porous structure of the considered layer because in this type of

This manuscript explores the approximate controllability of first order nonlinear hemivariational inequalities with non instantaneous impulses in a real Hilbert space. The proposed problem formulates a practical scenario by considering systems with non smooth and non convex behavior, while also incorporating the non instantaneous nature of impulses. To effectively model these dynamics, space of piecewise

In this paper, we propose and solve a novel Brinkman–triple–porosity–permeability model to describe fluid flow between filled conduits, matrix, micro-caves, and micro-fractures. The flow in triple-porosity media, consisting of three porosity types as matrix, micro-caves, and micro-fractures, is described by a fully coupled triple-porosity model, which removes the stated assumptions of sequential flow

This paper is mainly concerned with chaos, stability and bifurcation of a generalized Cohen-Grossberg neural network with two delays or one delay or without any delays.The network is proved to be chaotic in the sense of Li-Yorke by applying the snap-back repeller theory if it has one or two delays, and it is chaotic in the sense of Li-Yorke by using the coupled-expanding theory if the network has not

This paper investigates fixed-time bipartite synchronization of signed co-opetition coupled artificial delayed neural networks (CADNNs) under stochastic disturbances and time delays. To improve the quality of output signals, pth moment is considered into the research for stability synchrony of the signed co-opetition CADNNs. To reduce control costs and mitigate chattering during the bipartite synchronization

The optimal tracking control for unknown nonlinear systems via reinforcement learning (RL) is still an open problem in the absence of an initial stabilizing policy. Its fundamental challenge lies in improving poor learning efficiency, arising from an additional switching term. In view of such a difficulty, this paper proposes a dual-time-scale RL (DTSRL) algorithm by devising an alternate learning

This paper presents a novel region bounded observer designed for nonlinear systems modeled using Takagi–Sugeno (T-S) fuzzy frameworks. The proposed observer effectively estimates both the lower and upper bounds of the actual system dynamics even by taking external disturbances and measurement noise into account. To ensure both the non-negativity and Metzler properties, a membership-dependent Lyapunov–Krasovskii

This paper addresses the quasi synchronization problem for switched dynamic networks under unknown deception attacks. It is assumed that both the false information and the attack frequency of the deception attacks are unknown a priori. To tackle this, an attack-independent synchronization control method that consists of a stabilizing switching law and an event-triggered distributed control input is

The vibration of a gear system caused by mesh stiffness is generally recognized as one of the main sources of self-excited vibration of the system. Therefore, accurate calculation of the stiffness is extremely important for the study of the dynamics of the gear system. However, the parameters that calculate time-varying mesh stiffness (TVMS) calculation of straight bevel gears using potential energy

This paper presents a first attempt to address the distributed region-reaching control problems of multiple underactuated Euler–Lagrange systems (MUELSs) within an energy-shaping framework. An adaptive gain technique incorporating the region potential function is suitably introduced to design a distributed region-reaching control scheme by the best use of the passivity-based control (PBC) framework

Most existing prescribed performance boundaries are designed to be strictly monotonically decreasing, which may not always be advantageous. When control input fail to meet the prescribed performance requirements, strict monotonicity can lead to constraint failure and singularity problem. This paper proposes novel non-monotonic prescribed performance specifications for tracking control of input-limited

In this research, we tackle the challenge of coordinating a group of redundant robot manipulator systems, each governed by Lagrangian dynamics. The goal is to maintain a stable formation within a specified dynamic region while avoiding kinematic singularities. The key feature of the designed control algorithm is the proposal of a fully distributed controller. This controller utilizes two distributed

This paper investigated the finite-time attractivity and stability of an hybrid stochastic system with Markovian switching. Drawing upon the principles of stochastic processes and stochastic analysis, and employing multiple Lyapunov functions, we derived a more readily verifiablecondition that is sufficient for ensuring the finite-time attractivity and stability of such systems. In particular, this

The prime focus of this study is to explore the attack reconstruction and attack-compensator-based nonfragile control issues of the Takagi–Sugeno fuzzy chaotic Markovian jump systems in the midst of cyber attacks, gain fluctuations and external disturbances. Firstly, an intermediate variable is framed, which serves as the basis for the construction of an intermediate observer that concurrently estimates

This paper delves into the fixed-time synchronization (FxTS) issue for nonlinear coupling memristive neural networks (MNNs) through aperiodicallyally intermittent sliding mode control (SMC), with a particular focus on the fixed-time external synchronization of two nonlinearly coupling systems that incorporate time delays. Differential inequalities, crafted to apply aperiodically intermittent SMC, couple

Nonlinear energy sink (NES) is a lightweight nonlinear device that is attached to a primary system for passive energy localization into itself. In this paper, the energy transfer mechanism of the vibro-impact nonlinear energy sink (VI-NES) in continuous systems, and its consequences in vibration suppression is addressed. We uncovered the significance of a new distinctive energy transfer phenomenon

This paper investigates the fixed-time (FXT) synchronization issue of spatiotemporal Cohen-Grossberg neural networks (CGNNs) via aperiodic intermittent control (AIC). First, a new FXT stability criterion is established by using comparison principle, proof by contradiction and variable transformation methods, and a more accurate settling time (ST) is obtained through optimal value theorem, which is

In this paper, we propose two novel alternated multi-step inertial projection algorithms with self-adaptive step sizes. These algorithms are employed to solve the quasimonotone bilevel variational inequality problem (QBVIP, where VIP denotes a variational inequality problem) with a variational inclusion constraint in a real Hilbert space, where the QBVIP involves a strongly monotone mapping at the

Achieving high-performance, broadband, and multidirectional energy harvesting from ultralow-frequency vibrations presents significant challenges and remains a key research focus. This study introduces a bio-inspired 3D nonlinear limb-like mechanism that utilizes clamped bending-type piezoelectric beams to capture energy from vertical, horizontal, and in-plane rotational vibrations. Two configurations

This paper innovatively designs a novel prescribed-time zeroing neural network (ZNN) model to solve the time-varying complex Sylvester (TVCS) equation, with its implementation embedded within the context of the pseudo-inverse of a matrix. By incorporating a trigonometric function term into the activation function, the proposed prescribed-time ZNN model is capable of achieving zero convergence within

This paper focuses on the issue of the exponential synchronization in mean square (ESMS) of the multi-links time-delayed stochastic complex networks with Markovian switching (MTSCNM) through a novel intermittent adaptive dynamic event-triggered control (IADE-TC). First of all, the parameters within the event-triggered condition of the IADE-TC mechanism are associated with the adaptive strength, signifying

In this work, an ultra-local model-based prescribed-time hybrid force/position controller (UPTHC) is proposed for a 3-DOF series elastic actuator-based manipulator (SEAM) under input and output constraints. The UPTHC features a dual-loop structure, integrating force and position sub-control loops. By using the idea of admittance control, the force loop converts the interactive force control into position

This article explores the dynamics of rumor propagation on heterogeneous social networks, focusing on the evolution of rumor spread in the presence of dual media intervention. A novel stochastic model incorporating class-age structure, truth dissemination and time-varying stopping rate is proposed. Initially, a coupled deterministic system of ordinary and partial differential equations is developed

In this paper, we propose a modified Cucker–Smale system with nonlinear velocity couplings and intermittent control. Firstly, a novel lemma for finite-time and fixed-time stability has been formulated, applicable to systems with right-side discontinuities, with conditions that are more general and flexible compared to those in previous studies. Secondly, by imposing assumptions on the initial state

Since the nonphysical attraction force near the end of the recovery phase seriously distorts the impact behavior in the granular system, this investigation aims to develop three strategies to eliminate the nonphysical attraction force to improve the deficiency of the viscous contact force models. The optimization principle for removing the nonphysical attraction force of the viscous damping factor

Stochastic contact Hamiltonian systems are an important class of mathematical models, which can describe the dissipative properties with odd dimensions in random scenario. In this article, we investigate the dynamics of the systems via structure-preserving numerical methods. The contact structure-preserving schemes are constructed by the stochastic contact Hamilton–Jacobi equation. A general numerical

In this paper, the problem of adaptive secure control of a nonlinear servo system subject to state constraints, disturbance and denial-of-service (DoS) attacks is studied. An adaptive backstepping control scheme is developed. Firstly, a model of connected servo motors suffer from state constraints and disturbance is established. Then, in order to estimate the prior knowledge of the disturbance, a disturbance

In this paper, we study a nonlinear beam equation subject to an almost periodic forced term, which is analytic on t and x. Under appropriate assumptions on the perturbation, we show the existence of almost periodic solutions of such an equation and present a more precise analytical solution. The proof is based on the partial normal form and infinite-dimensional KAM (Kolmogorov–Arnold–Moser) theory

A stochastic HIV/AIDS model with a log-normal Ornstein–Uhlenbeck process is investigated, which incorporates screened disease carriers and active treatment. First, the global asymptotic stability of endemic equilibrium of the corresponding deterministic system is obtained when R0>1. Second, the existence of stationary distribution is examined by constructing a suitable Lyapunov function, which determines

In this paper, for the first time, we formulate and prove a Gronwall-type inequality for the general fractional integrals with the Sonin kernels and with variable coefficients. Most of the Gronwall-type inequalities for the Fractional Calculus operators introduced in the literature so far are particular cases of this inequality. In the second part of the paper, the Gronwall-type inequality for the

This paper investigates the well-posedness and numerical approximation of a nonlinear generalized fractional stochastic differential equation driven by multiplicative white noise. The proposed model generalizes conventional Caputo-type fractional stochastic systems by incorporating a kernel function ζ(t), which enables flexible characterization of memory effects and nonlocal interactions in complex

In this paper, we introduce two modified subgradient extragradient methods with two-inertial steps based on Halpern-type and Mann-type iterations for approximating solutions of variational inequalities involving quasi-monotone operators in real Hilbert spaces. The step-size of our proposed algorithms are designed to select self-adaptively without requiring the knowledge of the Lipschitz constant of

We set up a system of Caputo-type fractional differential equations for a reduced neuron model known as the denatured Morris–Lecar (dML) system. This neuron model has a structural similarity to a FitzHugh–Nagumo type system. We explore both a single-cell isolated neuron and a two-coupled dimer that can have two different coupling strategies. The main purpose of this study is to report various oscillatory

In this paper, we investigate a broad class of solutions of the B-type Kadomtseve-Petviashvili (BKP) equation by utilizing the Pfaffian τ-function. The fundamental solution is a linear periodic chain of lumps moving at separate group and wave velocities. We construct general linear arrangements for the BKP equation and give degenerate configurations such as parallel and superimposed lump chains. The

This paper considers the second order variable time-step DLN algorithm for the time-dependent Boussinesq equations. The considered numerical scheme maintains the following features: second order, decoupling, linearization and unconditional stability. In order to achieve the above mentioned merits, the semi-implicit scheme is adopted to treat the nonlinear terms, the stability results of numerical scheme

This research introduces a novel approach to analyze global exponential input-to-state stability for a category of nonlinear systems affected simultaneously by both unbounded distributed delays and time-varying neutral and transmission delays. The new method avoids constructing Lyapunov–Krasovskii generalized functionals. We verify the validity of the obtained results with two numerical examples. Notably

In this article, we investigate an electroacoustic resonator with a programmed cubic nonlinearity with constant and time-dependent coefficients. We design an experiment coupling an acoustic mode of a tube with a digitally programmable nonlinear resonator. Both simulations and experiments are carried out to compare optimized points for the resonator with programmed cubic nonlinearity with constant and

We prove an abstract KAM (Kolmogorov–Arnold–Moser) theorem constructed by Zhou (2017) in different ways and apply it to the nonlinear Schrödinger equation systems with real Fourier Multiplier. We prove the existence of a class of Whitney smooth small amplitude quasi-periodic solutions for more types of equation systems.

Nonlinear one-dimensional reaction–diffusion equations are useful for modeling processes in science and engineering. Non-classical symmetry analysis with a vanishing coefficient of ∂∂t is applied to search for non-Lie solutions of a class of nonlinear reaction–diffusion equations. The analysis leads to two non-classical symmetries. Each symmetry gives a solution that cannot be constructed using classical

This paper proposes an event-based uniform prescribed-time output feedback control (PTOFC) approach for irregular output-constrained nonlinear systems (OCNSs). Unlike the most existing methods of OCNSs, they mainly focus on OCNSs with infinite-time/deferred output constraints (i.e., the output constraints existing for all t≥0 or t≥t0), while many actual systems often suffer from irregular output constraints

In this study, we propose a predator–prey model incorporating impulsive density-dependent nonlinear pesticide spraying and the release of predators (natural enemy of the pest) at different fixed moments. The pest extinction semi-trivial periodic solution is derived. Further, global asymptotic stability of the obtained periodic solution and the permanence of the studied model are acquired. Depending

In this paper, we propose a three-level linearized difference scheme to solve the Rosenau–Burgers equation based on the double reduction order method and the fourth-order compact operator under the spatial periodic boundary conditions. We discuss the conservation law, solvability, and convergence for this difference scheme. The proposed scheme has second-order temporal and fourth-order spatial convergence

The evaluation of node centrality remains a critical challenge in the field of complex network research. This paper proposes a novel method, the JSD method, which integrates local and global information to measure node centrality. The method employs Shannon entropy to quantify local centrality and Jensen–Shannon (JS) divergence to compute inter-community distances, thereby assessing topological differences

This paper is concerned with the fault detection problem for a class of network systems composed of multiple clusters with unknown system matrices. Each cluster consists of multiple subsystems and the connections between clusters are unmeasurable. For these unmeasurable connections in network systems, traditional system identification and fault detection methods may be difficult to be directly applied

This paper proposes a new concept, continuous stochastic Lagrangian descriptor, to discern the hyperbolic structure for multiplicative noise saddle and beyond. The multiplicative noise saddle is proved to entail a random fixed point with exponential dichotomy. Analogous to the additive noise case, the hyperbolic structures, composed of the random fixed point together with its stable and unstable manifolds

A computational bifurcation diagram of nonlinear fractional order systems may provide a visual representation of understanding possible dynamics in a wide range of system parameters and associated fractional orders. This observed phenomenon has sparked new interest in the question of mathematically sound and rigorous proofs of the existence of such dynamics. No mathematical foundation for the stability

In this paper, we derive Hamilton–Pfaff-type partial differential equations (PDEs) by employing exterior differential techniques within the framework of a multi-dimensional fractional optimal control problem, incorporating principles from fractional calculus. This approach provides a rigorous analytical foundation for studying systems governed by non-integer order dynamics, thereby enhancing the understanding

This study presents a nonlinear dynamic analysis of bistable composite panels operating under time-varying centrifugal fields with harmonic perturbations. The research focuses on characterizing the asymmetric bifurcation phenomena and unidirectional snap-through mechanisms induced by rotational parameter variations. Theoretical modeling integrates first-order shear deformation theory with geometric

This study presents an in-depth analytical and numerical investigation of the modified Cairn–Tsallis-driven modulational instability of ion-acoustic waves in electronegative plasmas containing both positive and negative ions, as well as non-Maxwellian electrons. Using the reductive perturbation technique, the nonlinear Schrödinger equation governing the modulational instability dynamics of ion-acoustic

The nonlinear dynamic model of the compound planetary gear transmission system with cracks was established. The mesh stiffness of the cracked gears was solved using the energy method and the slice method, and nonlinear factors such as random wind speed, time-varying support stiffness, tooth surface friction, gear flexibility, and tooth side clearance were coupled into the compound planetary gear transmission

Due to the focusing of short or long waves, the solutions of dispersive equations may exhibit singularities at some point. In this article, we show that the dispersive blow-up phenomenon will occur to the solutions of three dimensional generalized Zakharov–Kuznetsov equations. Specifically, we construct smooth initial data such that the associated global solutions fail to be C1(R3) with origin as the

Analyzing the stiffening or softening effect on vibration in structures experiencing significant displacement due to external forces presents a formidable theoretical challenge. For this topic, the traditional methods employed by Rayleigh, Ritz, and Galerkin have proven inadequate. In response, this study introduces a novel theoretical framework to address this issue. The research highlights that rotational

In addition to radial rubbing, axial rubbing may also occur between the rotor and stator. However, in recent decades, greater attention has been devoted to the effects of base motion on the radial rubbing of rotating machinery. This paper investigates vibration characteristics induced by axial rubbing in a shaft-disk system considering the influence of base motion. A developed differential equation

The time-varying contact states at the contact interface introduced local nonlinear mechanical behaviors of the bolted joint rotor, especially under varying speed condition. In this study, a lateral-torsional coupled dynamic model of a bolted joint rotor system is established using the lumped mass method, and the Iwan model is employed to characterize the interface contact behavior. The influence of