In this paper, we present an arbitrarily high-order numerical scheme for the two-component Camassa–Holm system, ensuring the preservation of three invariants: energy and two Casimir functions. The spatial discretization is achieved using Fourier–Galerkin methods, resulting in a semi-discrete system which retains a Hamiltonian structure and approximates the invariants of the original continuous system

In ecological and ecosystem studies, spatiotemporal distribution patterns are identified as crucial factors in maintaining species diversity. Specifically, spiral waves, which are a typical spatiotemporal pattern, are prevalent across various ecosystems, including both continuous and discrete-time systems. In continuous-time systems, spiral waves are commonly associated with Hopf bifurcations. This

In this paper, we explore a class of time-dependent mixed quasi-variational-hemivariational inequality problems (TMQVHVI), which are characterized by the dependence of their constraint set on the solutions. We prove a solvability result for TMQVHVI by using a static mixed quasi-variational–hemivariational inequality and a measurable selection lemma. And, moreover, the boundedness and closedness of

We investigate the dynamics of maps of the real line whose behavior on an invariant interval is close to a rational rotation on the circle. We concentrate on a specific two-parameter family, describing the dynamics arising from models in game theory, mathematical biology and machine learning. If one parameter is a rational number, k/n, with k,n coprime, and the second one is large enough, we prove

The Local Randomized Neural Networks with Discontinuous Galerkin (LRNN-DG) methods, introduced in Sun et al. (2024), were originally designed for solving linear partial differential equations. In this paper, we extend the LRNN-DG methods to solve nonlinear PDEs, specifically the Korteweg–de Vries (KdV) equation and the Burgers equation, utilizing a space–time approach. Additionally, we introduce adaptive

This paper introduces a novel varying-coefficient autoregressive model that includes an explanatory variable and a non-stationary state equation to analyze and predict complex time series data. The model incorporates a function that evolves over time, which provides a sophisticated understanding for analyzing data with nonlinear and non-stationary characteristics. Some key statistical properties of

This paper deals with an intergenerational utility maximization problem for consuming a naturally exhaustible resource. In this context, we are at odds with the unfair standard procedure of applying a time-dependent factor for discounting the utility and introducing a suitable function for penalizing overconsumption. A finite-time horizon dynamic stochastic optimization problem is presented to achieve

We discuss the synchronization control problem for a network of Euler–Bernoulli beam equations with freedom at both ends and time-varying disturbances at the boundary. First, we present the aim of the control of this paper. Next, the reference signal is provided, allowing us to transform the control objective into a form that includes the virtual reference signal. Then, by the method of active disturbance

In this study, we introduce two recent algorithms designed to solve the split variational inclusion problem in Banach spaces by using two inertial extrapolations and self-adaptive step size technique. Theoretical analysis demonstrates that the inertial Mann-type self-adaptive algorithm (IMSA) and the inertial Halpern-type self-adaptive algorithm (IHSA) generate strong convergence under the specified

The use of conventional cubic nonlinear energy sink (NES) to mitigate vortex-induced vibrations has been widely investigated. Recently, bistable NES (BNES) has gained considerable attention owing to its ability to execute large amplitude inter-well motion and thus enhance energy transfer. But, the efficacy of BNES to mitigate self-excited vibrations in general and vortex-induced self-excited vibrations

This work presents a systematic characterization of the quasi-periodic dynamics of a uniaxial anisotropic magnetic nanoparticle under the influence of a time-varying external magnetic field. Using the Landau–Lifshitz–Gilbert (LLG) formalism, we analyze the response of the system as a function of key parameters, particularly focusing on the effects of magnetic anisotropy and dissipation. Through an

The exponential stability of the Caputo fractional order impulsive switched system (CFOISS) consisting of stable and unstable subsystems is addressed in this paper. We integrate the multiple Lyapunov function (MLFs) approach, the mode-dependent average dwell time (MDADT) method, and the fast-slow switching concept to handle the switched sequence. In order to better represent the impulse, we further

In Wu et al. (2021), Wu et al. studied an SIR epidemic model incorporating infection–age structure and spatial diffusion. It focused on the existence of traveling wave solutions when the diffusion coefficients met a technical condition (i.e., d3≤2d2). Moreover, the question of the existence of traveling wave solutions with c=c∗ remains open. This paper employs an approach rooted in the Schauder’s fixed-point

In this work, a new QGCD iterative algorithm is presented for finding the solution of a class of quaternion matrix equation. It is proved that if the studied quaternion matrix equation is consistent, the constructed algorithm can obtain the solution within finite iterative steps in the absence of round-off errors. Moreover, if the investigated quaternion matrix equation is inconsistent, the constructed

A novel high-order numerical method, specifically designed to preserve the mass and energy invariants of the coupled nonlinear Schrödinger equation (CNLS) is introduced. This algorithm integrates Gauss collocation schemes for temporal discretization with finite element methods for spatial discretization, enhanced by a post-processing correction procedure that ensures mass and energy conservation at

This work deals with tailored reduced order models for bifurcating nonlinear parametric partial differential equations, where multiple coexisting solutions arise for a given parametric instance. Approaches based on proper orthogonal decomposition have been widely investigated in the literature, but they usually rely on some a-priori knowledge about the bifurcating model and lack any error estimation

This paper delves into the network security issues of cyber–physical systems (CPSs), where malicious agents can launch distributed denial-of service (DDoS) attacks to disrupt communication channels between sensors and remote estimator. Addressing the strategic interaction between defenders and DDoS attacker, we establish a two-player zero-sum stochastic game framework that portrays the interaction

In this paper, we propose a method of the mixture-of-experts (MoE) model embedded with physics-informed neural networks (PINNs) for the hyperbolic conservation laws. The issue on solving hyperbolic conservation laws with PINNs is still challenging since the solutions of conservation laws may contain discontinuities. PINNs, as functional approximators, nearly fail in such cases, and numerical solutions

The objective of this paper is to investigate mixed set-valued stochastic differential equations with fractional Brownian motion, where the diffusion term is also set-valued. Under the non-Lipschitz continuity conditions, firstly, some new and reliable lemmas about the set-valued stochastic integral are provided. Secondly, we justify the existence and uniqueness of solutions to considered equations

This paper investigates the tracking control problem for the uncertain fractional-order nonlinear systems (FONSs) with unmeasured states and unknown control gain subject to external disturbances and actuator fault, under restricted communication resources. First, the radial basis function neural networks (RBF NNs) are deployed to identify the unknown smooth nonlinear function. Subsequently, a neural

This paper proposes a decentralized event-triggered control scheme based on reinforcement learning to stabilize a class of partially unknown nonlinear mismatched interconnected systems with time-varying state constraints and asymmetric control input constraints. First, a meticulously designed barrier function, which combines traditional and smoothing functions, transforms a constrained interconnected

The extragradient method is an efficient approach for solving variational inequality problems. In this paper, we propose two kinds of inertial viscosity extragradient methods with new step sizes for tackling variational inequality problems characterized by pseudomonotone and Lipschitz continuous cost operator in real Hilbert spaces. Notably, these algorithms necessitate the computation of just a single

Neural synchronization plays a crucial role in understanding complex brain functions and driving advancements in artificial intelligence. This paper investigates the Mittag-Leffler projective synchronization in Caputo fractional-order memristive neural networks with reaction–diffusion dynamics and multiple time-varying delays. To address parameter mismatches and achieve synchronization, two adaptive

Using a dataset of stars from a barred galaxy that provides instantaneous positions and velocities in the sky, we propose a method to identify its key structures, such as the central bar and spiral arms, and to determine the bar pattern speed in the short term. This is accomplished by applying combinatorial and topological data analysis techniques to the available star-state information set.

This paper concentrates on the H∞ sliding mode optimal control (SMOC) problem for nonlinear systems with mismatched interference and constrained input. Firstly, an adaptive-triggered strategy for the discontinuous control part is employed, which can suppress input interference and the separated matched disturbances. Also, the system trajectories are guaranteed to converge to the sliding manifold. Moreover

Entropy and mutual information rates are key concepts in information theory that measure the average uncertainty and statistical dependence growth between two stochastic processes, respectively. This paper introduces a distance rate measure for discrepancy growth between two stationary processes, termed the Jensen-distance rate (JDR), which is based on spectral and cross-spectral densities. I examine

This paper deals with an inertial proximal algorithm that contains a Tikhonov regularization term, in connection to the minimization problem of a convex lower semicontinuous function f. We show that for appropriate Tikhonov regularization parameters the value of the objective function in the sequences generated by our algorithm converge fast (with arbitrary rate) to the global minimum of the objective

This is a classical problem in mathematical physics to describe the dynamics of large-scale multi-agent systems. In this paper, we propose a limit graphon integral-differential system with a weight feature of graphon to represent a large-scale second-order delay multi-agent system, where the time delay represents transmission time lags. We first study the well-posedness, stability, and regularity of

This paper focuses on the Euler–Maruyama (EM) scheme for delay-type stochastic McKean–Vlasov equations (DSMVEs) driven by fractional Brownian motion with Hurst parameter H∈(0,1/2)∪(1/2,1). The existence and uniqueness of the solutions to such DSMVEs whose drift coefficients contain polynomial delay terms are proved by exploiting the Banach fixed point theorem. Then the propagation of chaos between

How to design control algorithms to effectively regulate the collective behavior with sensing delay remains a formidable challenge. In this paper, we propose to use bifurcation control with PD controller to regulate the collective behavior under sensing delay. The controlled system exhibits the emergence of three distinct states. Bifurcation analysis reveals that the Hopf bifurcation and pitchfork

This paper explores the mean-square bounded synchronization problem of leader-following multi-agent systems (LF-MASs) with directed graph under dual-channel stochastic switching deception attacks. Compared to previous studies, a new dual-channel stochastic switching deception attack mode is considered. Under this attack mode, the actuator receives different deception signals sourced from either the

Global optimization is a topic of great interest because of the many practical problems in real life. This article focuses on the unconstrained global minimization of multi-modal continuously differentiable functions, an important subclass of global optimization problems. In order to solve these problems, we develop a new global optimization technique that utilizes two fundamental concepts. The first

In cooperative systems, information exchange is essential for achieving consensus, and the preservation of data privacy has attracted growing attention. However, most existing studies have been limited to first-order multi-agent systems. This study investigates the privacy-preserving consensus problem of second-order agents with Lipschitz-type nonlinearities. A novel masking scheme based on specific

Consider the Neumann problem: −Δu−μ|x|2u+λu=|u|q−2u+|u|p−2uinR+N,N≥3,∂u∂ν=0on∂R+Nwith the prescribed mass: ∫R+N|u|2dx=a>0,where R+N denotes the upper half-space in RN, 1|x|2 is the Hardy potential, 20, ν stands for the outward unit normal vector to ∂R+N, and λ appears as a Lagrange multiplier. Firstly, by applying Ekeland’s variational principle, we establish the existence of normalized solutions that

This paper aims to discuss the existence, uniqueness and continuous dependence of mild solution of a class of non-autonomous stochastic neutral functional differential equations with state-dependent delay. Firstly, by using operator theory and estimates of the nonlinear term, we obtain the existence, uniqueness and continuous dependence of our concern system. Secondly, through the Arzelà–Ascoli theorem

This paper focuses on the research of nonlinear distributed parameter cyber physical systems (DP-CPS) via finite-time interval. The nonlinearity of the DP-CPS is captured through the utilization of the Takagi–Sugeno (T–S) fuzzy model, which gives rise to a class of fuzzy parabolic partial differential equation (PDE). In order to optimize the network resources, a class of dynamic quantizer is employed

Breast cancer remains one of the most prevalent and life-threatening diseases worldwide, necessitating mathematical modelling frameworks to capture the complexity of its progression and risk factors. This research endeavor uncovers the novel machine learning expedition using an Adaptive Nonlinear AutoRegressive eXogenous (ANARX) neural network on a Fractional Order Breast Cancer Risk (FO-BCR) model

The objective of this paper is to consider the asymptotical behavior of solutions for the two-dimensional partial dissipative Boussinesq system with memory and additive noise. We first establish the existence of a random absorbing set in the phase space. However, due to the presence of the memory term, we cannot obtain some kind of compactness of the corresponding cocycle through Sobolev compactness

We present a methodology for computing normal forms in discrete systems, such as those described by Poincaré maps. Our approach begins by calculating high-order derivatives of the flow with respect to initial conditions and parameters, obtained via jet transport, and then applying appropriate projections to the Poincaré section to derive the power expansion of the map. In the second step, we perform

A H1-Galerkin mixed finite element method (MFEM) is explored for solving the nonlinear Klein–Gordon equation, utilizing the lower-order bilinear element paired with the zero-order Raviart–Thomas element (Q11+Q10×Q01). The existence and uniqueness of the solutions for the discretized system are rigorously established. By exploiting the integral identity associated with the bilinear element, a superconvergence

This paper proposes a new approach for analyzing extinction conditions in multi-stage epidemic models, incorporating stochastic noises to account for sudden environmental or population-level changes that influence infection transmission. By utilizing an (n+1)-dimensional perturbed system that captures both gradual amelioration and proportional jumps, the research establishes sharp extinction criteria

Propagation problems of reaction fronts in viscous fluids are crucial in many industrial and chemical engineering processes. The interactions between the reaction properties and the fluid dynamics yield a complex and nonlinear model of Navier–Stokes equations for the flow with a strong coupling with two reaction–advection–diffusion equations for the temperature and the degree of conversion. To alleviate

In this article, we investigate the nonlinear spectral properties of the coupled third-order flow of the Kaup–Newell (TOFKN) system by formulating a local matrix ∂̄-equation with non-normalized boundary conditions and two linear constraint equations. Furthermore, we derive a coupled Kaup–Newell hierarchy with sources using recursive operator. By employing a specially designed spectral transformation

We showcase the utility of the Lagrangian descriptors method in qualitatively understanding the underlying dynamical behavior of dynamical systems governed by fractional-order differential equations. In particular, we use the Lagrangian descriptors method to study the phase space structure of the unforced and undamped Duffing oscillator when fractional-order differential equations govern its time evolution

This research presents a novel quantized fuzzy control technique based on Luenberger-like disturbance observer for a class of nonlinear delayed parabolic partial differential equation (PDE) systems, which are influenced by two distinct types of disturbances. To begin with, the PDE system is decomposed using the Galerkin approach, resulting in a finite-dimensional slow ordinary differential equation

This paper studies the exponential stabilization issue of memristive neural networks (MNNs) in the presence of denial-of-service (DoS) attacks by using an event-triggering scheme. Unlike the existing event-triggering strategies, not only does the devised resilient discontinuous event-triggering (RDET) scheme avoid the Zeno phenomenon and reduce network communication resource utilization, but can it

The transport of regolith material has been confirmed by in situ exploration missions to asteroids like Itokawa, Ryugu and Bennu, providing evidences for the topographic evolution of these minor planets. This paper studies the migration of disturbed regolith materials across the asteroid surface from the viewpoint of nonlinear dynamics. We propose a simplified two-dimensional model that captures the

The maximum bound principle (MBP) is a crucial characteristic for a board class of semilinear parabolic equations, making it essential to preserve this feature in numerical simulations, particularly for problems involving degenerate mobility and logarithmic potential function. In this paper, we focus on the nonuniform second-order backward differentiation formula (BDF2) for the Allen–Cahn (AC) model

Most marine and plant species exhibit two main life stages: a dispersing stage and a sedentary stage. These stages significantly influence the species’ spatial distribution and abundance patterns. To accurately depict the spatial patterns of these species, this paper investigates a hybrid system that combines parabolic and hyperbolic elements, effectively differentiating between the dispersal and sedentary

In order to improve an existing classical virtual element for the fourth-order elliptic problem, we propose a special class of quasi-orthogonal polynomials and then construct a new type of numerical integration formula based on the polynomials. The special feature of the formula is that it uses the function values and the derivative values of the integrand at the endpoint of the interval, which is

The article presents a method to stabilize the attitude of a rigid body in the presence of measurement noise and delayed feedback on the nonlinear manifold TSO(3). It is assumed that the measurements of angular velocity and attitude are influenced by a bounded white noise process. The analysis of such a system cannot be done with ordinary differential equations, but stochastic functional differential

As circuits continue to shrink in size, noise has emerged as a critical challenge in achieving optimal performance. Stochastic resonance in logic circuits offers an innovative approach to harness noise constructively; however, current implementations are limited to basic logical functions such as OR, AND, NOR, and NAND, restricting broader applications. This paper introduces a three-dimensional (3D)

This paper aims to study the multi-physics coupling interaction mechanism between thermal, lubrication and dynamics of bearings. Firstly, considering the influence of clearance, the load distribution integral is introduced to evaluate the non-uniform load characteristics of the bearing. On this basis, the bearing point contact lubrication model was established based on elastohydrodynamic lubrication

By using a formulation of a class of compressible viscous flows with a heat source via vorticity and expansion-rate, we study the Oberbeck–Boussinesq flows. To this end we establish a new integral representation for solutions of parabolic equations subject to certain boundary condition, which allows us to develop a random vortex method for certain compressible flows and to compute numerically solutions

The rotating shaft-disk-blade system(RSDBS) is the crucial part of turbomachinery. Among RSDBS, crack is the most common failure mode of the blade. The crack propagation is affected by many factors such as stress state and environmental conditions, leading to the randomness of the crack angle. This study focuses on the dynamic modeling and analysis of the three-dimensional blade tip clearance (3D-BTC)

Modeling studies associated with absence epilepsy often consider neural circuits and neglect the critical involvement of glial cells. Recently, the view that astrocytes are new targets for the treatment of epilepsy has received increasing attention. Based on the established basal ganglia-corticothalamic (BGCT) mean-field model involving glutamate (GLU) dynamics in the extracellular space of cerebral

This study investigates the nonlinear dynamic behavior and snap-through instability of shallow sandwich arches under a moving point load. The arches comprise an open-cell Kelvin foam core sandwiched among nanocomposite face sheets strengthened by graphene platelets (GPLs), featuring functional grading. The foam characteristics are obtained by considering the bending, twisting, and stretching of cell

In order to understand how advection and human behaviors affect dynamics of cholera transmission, we focus on a reaction–diffusion–advection cholera model in a heterogeneous environment, where human behavior change describes the reliance on contaminated water sources and advection reflects spread of cholera along a theoretical river. We first show the well-posedness and then get the global dynamical

In this paper, the optimization problem of uncertain nonlinear multiagent systems is studied. It is important to note that the control directions of the studied systems are unknown. By designing a suitable state transformation, the nonlinear multiagent systems with unknown control directions are transformed into the nonlinear multiagent systems with known control directions. However, the states of