Exploring chaotic systems via Poincaré sections has proven essential in dynamical systems, yet measuring their characteristics poses challenges to identify the various dynamical regimes considered. In this paper, we propose a new approach that uses image processing to classify the transport regime. We characterize different transport regimes in the standard map with the proposed method based on image

We study a fluid-surfactant phase-field system under two types of fluid flow models: one consisting of two Cahn–Hilliard equations coupled with the Navier–Stokes equations, and the other consisting of two Cahn–Hilliard equations coupled with the Darcy equations. We apply the scalar auxiliary variable approach and the pressure correction method to develop a linear, fully decoupled, and second-order

The influence of multiplicative white noise on the resonance capture of strongly nonlinear oscillatory systems under chirped-frequency excitations is investigated. It is assumed that the intensity of the perturbation decays polynomially with time, and its frequency grows according to a power low. Resonant solutions with a growing amplitude and phase, synchronized with the excitation, are considered

This paper delves into the stabilization of Boolean control networks (BCNs) through leveraging ideas from event-triggered output feedback control and the Ledley antecedence solution methodology. Initially, one necessary and sufficient criterion is proposed to examine the stabilization of BCNs via the reachable sets established by Ledley antecedence solution. Subsequently, based on the reachable set

This paper investigates the prescribed-time tracking synchronization (PTS) of Kuramoto oscillator networks (KONs) with directed graphs. Existing control protocols for achieving KONs’ synchronization within a finite time are based on linear or power functions of phase differences, but they ignore the 2π-periodicity of phase oscillators. This leads to desynchronization and dramatic phase changes, increasing

This paper is devoted to decentralized sampled-data H∞ fuzzy filtering with exponential time-variant gains (ETGs) for nonlinear interconnected systems subject to uncertain interconnections. Both the interconnected system and the desired decentralized filter are modeled as Takagi–Sugeno fuzzy systems. An alternative approach to the usual coordinate transformation method is introduced to design the fuzzy

Exponential synchronization for a class of delayed discontinuous complex-valued neural networks (CVNNs) with leakage delay and diffusion effects is investigated in this paper. First, CVNNs are separated into real and imaginary parts, an equivalent real-valued subsystems are obtained for the analysis. Then, some novel and flexible algebraic criteria are established to ensure the exponential synchronization

This work addresses the study of dynamics and bifurcations in a prey–predator model, known in the literature as the Holling–Tanner model, subject to a harvesting action of predators that is activated when the prey population is less than a certain threshold, and stopped otherwise. Such a model is represented by a piecewise smooth system with a switching boundary given by a straight line that is defined

This paper studies the exponential H∞ output synchronization of time-delay heterogeneous multi-agent systems (TDHMASs) with switching topology. The TDHMAS simultaneously considers switching topology, node delay, and dimensional heterogeneity. Without directly using the information of the leader, a mode-dependent dynamic controller is designed based on each agent’s internal compensation term derived

Certain Lyapunov conditions for the finite-time stability (FTS) and global FTS of a general nonlinear disturbed fractional ordered system is established initially. A settling time depending on the initial conditions of the system is introduced ensuring the FTS of the system and the result is then extended to global FTS. Secondly, FTS of a fractional ordered nonlinear disturbed neural network is examined

This paper uses analytical methods, including mode-matching techniques and Fourier transforms, to model sound sources in waveguides, particularly in scenarios with structural variations and sound-absorbent materials. The effectiveness of these methods in solving the governing boundary value problem is demonstrated, particularly focusing on understanding sound power output from monopole sources in pipes

Considering the issue that the current fixed-time stability theory has a setting-time upper bound far greater than the actual stability time, an improved fixed-time control scheme with a more compact setting-time upper bound is proposed. This scheme combines passive fault-tolerant control (FTC) and adaptive fuzzy technology to design an adaptive fuzzy fixed-time fault-tolerant controller that addresses

This article investigates the synchronization issue of stochastic large-scale networks with time delays (SLNTD) via periodic self-triggered asynchronous intermittent sampled-data decentralized control (PAISC). This is the first implementation of asynchronous decentralized control to tackle asynchronization challenges in intermittent sampled-data control. Particularly, the self-triggered characteristic

The high-rise buildings are prone to vibration due to external disturbance. To ensure residents’ lives and property security, the vibration suppression problem of high-rise buildings has attracted extensive attention from researchers. As a large flexible structure, the high-rise building is more accurate in modeling and control using partial differential equations (PDE). Based on the nonlinear PDE

This paper investigates the event-triggered consensus control of deterministic nonlinear multi-agent systems (MASs) within the context of Denial-of-Service (DoS) attacks. In such adversarial scenarios, malicious attackers possess the potential to pilfer sensitive data by effectively distracting the security apparatus via DoS attacks. Although the consensus problem of MASs under DoS attacks has been

In this paper, the mean-square finite-time stability (MSFTS) and mean-square prescribed-time stability (MSPTS) of a class of nonlinear stochastic parabolic distributed parameter systems are studied. An internal dynamic variable is introduced to design dynamic periodic event-triggered mechanism (DPETM) for FTS. Moreover, a new prescribed-time DPETM is proposed by combining two different adjustment functions

In this paper we study a basic model of economic growth where we integrate a zero-dimensional energy balance model of the earth. The albedo of the earth, which determines the share of reflected sunlight, is a piecewise smooth function of the average surface temperature. Thus, we take into account possible feedback effects of a higher temperature. The analysis of the model shows that the model with

In this paper, an efficient numerical algorithm is proposed to solve the convection problem in the superposition of incompressible flow and porous media flow. The displayed numerical method is a first-order γ-scheme of linear multi-step methods plus time filter algorithm(LMTF), and can effectively increase the convergence order from the first order to the second order with almost no increasing in computation

In this work, we propose a novel class of mass- and energy-conserving schemes formulated on arbitrary polygonal meshes for the coupled nonlinear Schrödinger–Helmholtz system. This approach leverages the Crank–Nicolson time discretization and the virtual element method for spatial discretization. To establish the theoretical foundation, we use the duality argument to estimate the difference quotient

To study the motion reliability and dynamic characteristics of a planar multi-bar mechanism with clearance, this paper takes the R-2RRP-RRR mechanism with single clearance as the research object, establishes its dynamic model based on the Newton-Euler method, and the effectiveness of the dynamic model is verified through both the numerical computation and multibody dynamics simulation. A method for

The vibro-impact system has more complex and variable dynamic behavior, and its research has attracted the attention of many scholars. However, the effect of resonance on the dynamic characteristics of vibro-impact systems is rarely explored. In this paper, the parametric resonance and stochastic stability of a vibro-impact system excited by bounded noise parameters are investigated. For weak noise

The main objective of this paper is to consider an optimal distributed control problem for a reaction–diffusion model with tumor-immune interactions, which consists of a coupled system of reaction–diffusion equations for normal cells, tumor cells, immune cells and chemotherapeutic drug. Moreover, a suitable distributed control variable representing the concentration of cytotoxic drugs in medical treatment

Integrated Electric Drive Systems (IEDS) are widely used in electric vehicles due to its compact design and high-power density. To address the issue where nonlinear excitations and variable, complex operating conditions of IEDS can exacerbate high and low-frequency torsional vibrations, leading to decreased reliability of the IEDS. The active dual-layer suppression method is proposed based on analyzing

This study comprehensively investigates the influence of the rotation effect on the elastic field of functionally graded (FG) hollow cylinders and annular disks with considering uncertainty and fluctuation in material parameters. The multilayer heterostructure power-law inhomogeneous (MHPI) model is introduced, where the radial change in Young's modulus and density are approximated by multiple sublayers

We explore the dynamics of modulational instability (MI) in PT-symmetric fiber Bragg gratings, focusing on the intermodulation phenomenon known as four-wave mixing (FWM). While the role of FWM has been already studied in conventional systems, introducing equal amount of gain and loss, which are the key elements of PT-symmetric notion, leads to intriguing new outcomes. Notably, it results in an unprecedented

Tumor cell migration within the microenvironment is a crucial aspect for cancer progression and, in this context, hypoxia has a significant role. An inadequate oxygen supply acts as an environmental stressor inducing migratory bias and phenotypic changes. In this paper, we propose a novel multi-scale mathematical model to analyze the pivotal role of Snail protein expression in the cellular responses

The clearance joints and flexible components are crucial factors influencing the dynamic characteristics of mechanisms. Previous studies mainly focus on the dynamic response of simple mechanisms, with limited research on the dynamics analysis and chaotic behavior of complex spatial multi-body systems. To study the dynamic response of the Variable Stator Vane (VSV) mechanism, a nonlinear dynamic model

The utilization of low-frequency vibrations distributed in nature to provide energy supply for microelectronic devices has drawn greater attention. Based on the principle of flapping wings of insects, a bionic flapping wing bistable energy harvester (BFBEH) for low-frequency vibration is proposed by using a symmetrical flexible cantilever beam mounted with piezoelectric fibers to simulate the wings

This paper investigates the problem of finite and fixed time synchronization for multi-link complex-valued complex networks (MLCCNs) with time delay. In contrast to the existing works, the finite and fixed time synchronization of MLCCNs is conducted in the complex field, which is more general. In order to reduce the control costs, two hybrid control strategies, with finite time and fixed time, are

The theory of rarefied flow stability analysis provides essential theoretical support for predicting high-altitude transitions in aircraft and enhancing the performance of micro-electro mechanical systems (MEMS), offering significant scientific and engineering value. This paper introduces a linear stability analysis method based on a finite difference method of the Boltzmann-BGK model, applicable to

We propose an efficient computational algorithm for simulating incompressible fluid flows on a virtual cubic surface. By neglecting the influence of gravitational force, we effectively eliminate its impact on the system. Therefore, the dynamics can be characterized as essentially two-dimensional (2D) and confined to a plane. A projection method and a finite difference method (FDM) are used to numerically

This paper considers the consumption and portfolio optimization problems with recursive preferences in both infinite and finite time regions, in which the financial market consists of a risk-free asset and a risky asset following a general stochastic volatility process. By using Bellman’s dynamic programming principle, the Hamilton–Jacobi–Bellman (HJB) equation is derived for characterizing the optimal

This paper focuses on the dynamic behavior of a single-species model with two cognitive perceptual functions in a toxic environment, to simulate the different responses of fish to environmental changes. We first performed a spectral analysis of the model to obtain an eigenvalue problem for the stability of the constant steady state solution of the model. Then, Turing bifurcation analysis and Hopf bifurcation

In this work, we study the fixed points of multi-state networks over a complement-closed set X, a wide generalization of Boolean networks and some types of multi-state networks. We particularly focus on MAX (and MIN) multi-state networks, whose corresponding graph is undirected and all self-loop, and where the global evolution operator is induced by a disjunction (or conjunction) of direct and complemented

Chaotic systems exhibit self-similarity as a manifestation of their inherent complexity. In this paper, it is found that the spatial ergodic trajectories of chaotic systems exhibit consistent traversal behaviors across different spatial scales, manifesting power-law scaling: β(ɛ)∝ɛ−d with d>1. Here, d is introduced as a novel metric of fractal dimensions termed the Spatial Ergodicity Dimension (DE)

In the study of influence maximization, most existing research often assumes a one-off resource allocation at the start of a competition. As a result, they overlook the benefits of dynamic, time-sensitive strategies. To overcome this limitation, we propose a novel approach using inter-temporal allocations within a non-progressive voter model to optimize the timing and distribution of limited resources

Chaotic diffusion is a type of deterministic diffusion wherein Brownian-like behaviors stem from deterministic dynamics. We investigate the density evolution of delay-induced chaotic diffusion in this article. The density path evolving from initial conditions with a prescribed probability distribution is monitored. A Liouville-like continuity equation within which the velocity field is a gradient field

Based on the complexity of mosquito-borne disease transmission, the dependence of the transmission rate of pathogens on their load in mosquitoes and the variability of the ranges of different populations in space, we formulate a partially degenerated reaction–diffusion model that incorporates the age structure and general incidence to study the transmission of pathogens between mosquitoes and humans

This research show a way to adopts the perspective of phase-field crystal (PFC) models to study the superconductivity, under the theoretical framework of the dynamics of density functional theory (DDFT). We presents numerical solutions of two-dimensional (2D) patterns obtained from conserved Swift–Honhenberg equation with a non-potential form. The numerical simulations performed is related with the

In this paper, we consider the following Schrödinger–Choquard system in RN(−Δ)psu1+(V1(ɛx)−λ1)|u1|p−2u1=μ1[1|x|N−α∗F1(u1)]f1(u1)+βr1|u1|r1−2u1|u2|r2inRN,(−Δ)psu2+(V2(ɛx)−λ2)|u2|p−2u2=μ2[1|x|N−α∗F2(u2)]f2(u2)+βr2|u1|r1|u2|r2−2u2inRN,∫RN|u1|pdx=a1p,∫RN|u2|pdx=a2p,where (−Δ)ps is the fractional p-Laplacian operator, α∈(0,N), s∈(0,1), r1,r2>1, r1+r2∈(p,p+p2sN), ɛ>0 is a parameter, μi,ai>0(i=1,2) and β>0

This research aims to establish the sufficient conditions for the existence of the mild solution and approximate controllability for a class of Ψ-Caputo fractional neutral-type integro-differential stochastic inclusions with infinite delay in a separable Hilbert space. In the proposed stochastic control system, the Ψ-Caputo fractional derivative is considered, which has the flexibility to choose a

We consider a large class of variable exponents double phase differential inclusions with mixed boundary conditions in a bounded domain with Lipschitz boundary. The motivation behind studying this problem is that it may be used in modelling the antiplane shear problem of a long cylinder, made of an anisotropic nonlinear Hencky-type material, in contact with a rigid obstacle. We derive a variational

This paper focuses on the fusion filtering problem for a class of multi-sensor nonlinear rectangular descriptor systems with random transmission delays by considering the feedback fusion information. The random transmission delays are modeled by homogeneous Markov chains. For the feedback channel, a dynamic event-triggered mechanism is used to determine whether the information from the fusion center

This article investigates the issue of finite-time stabilization for fractional-order switched nonlinear system (FOSNS) under the novel framework of mode-dependent event-triggered mechanism (MDETM). Initially, this study effectively addresses Zeno behavior (ZB) avoidance in FOSNS by the MDETM approach. This mechanism operates through the strategy of event-triggered impulsive control (ETIC) and the

In this paper, a class of constrained fractional optimization problems under a dynamic system involving the ψ-Caputo fractional derivative is introduced. A computational method based on the modified hat basis functions is developed to solve these problems. This work is done by obtaining a new operational matrix for the ψ-Riemann–Liouville fractional integral of the modified hat functions. The established

We consider the Kuramoto-type models for associative-memory networks and its applications in binary pattern retrieval and classification. In this model, the coupling function consists of a Hebbian term and a second-order Fourier term with nonnegative parameter. The theory of the stability/instability has been established in literature for the equilibria corresponding to binary patterns. In this short

Stochastic wave equations with multiplicative fractional Brownian motions (fBms) provide a competitive means to describe wave propagation process driven by inner fractional noise. However, regularity theory and approximate solutions of such equations is still an unsolved problem until now. In this paper, we achieve some progress on the regularity and strong convergence of numerical approximations for

Three-dimensional (3D) volume reconstruction remains a fundamental technique with wide applications in fields such as 3D printing, medical diagnostics, and industrial design. This paper presents two novel lower boundedness-preserving auxiliary variable methods designed for the phase-field model of 3D narrow volume reconstruction. By employing scattered point data, our approach reconstructs smooth narrow

In this paper, we focus on the traveling waves for a perturbed generalized Bogoyavlenskii coupled system with delay convection term and weak dissipation, including periodic waves, solitary waves, kink and anti-kink waves. The corresponding traveling wave equation can be transformed into a 4-dimensional dynamical system, which is regarded as a singularly perturbed system and is reduced to a near-Hamiltonian

In this paper, we study the number of isolated crossing periodic orbits, so-called crossing limit cycles, for a class of piecewise smooth Kolmogorov systems defined in two zones separated by a straight line. In particular, we study the number of crossing limit cycles of small amplitude. They are all nested and surround one equilibrium point or a sliding segment. We denote by MpKc(n) the maximum number

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.

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

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

This paper is devoted to the qualitative theory of a class of fractional switched systems with a variable-time switching mechanism (FSSVT). FSSVT is a new class of state-feedback fractional switched systems, where the active regions of each subsystem vary with time. Initially, we obtain the condition of the existence and uniqueness of the global solution for FSSVT and give a criterion for determining

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

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

Nonlinear energy sink (NES) has been extensively investigated as typical nonlinear dynamic vibration absorber (NDVA) in engineering applications. However, the existing study primarily focuses on the normal operational conditions of mechanical equipment, overlooking considerations for abnormal operating conditions. This study aims to assess the vibration reduction effect of NES and tuned mass damper

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

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

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