This paper presents a two-grid finite element method for solving semilinear fractional evolution equations on bounded convex domains. In contrast to existing studies that assume strong regularity for the exact solution, our approach rigorously addresses the limited smoothing properties of the fractional model. Through a combination of semigroup theory and energy estimates, we derive optimal error bounds

We study a general class of bivariate fractional integral operators, derived from bivariate analytic kernel functions by a double substitution of variables and a double convolution. We also study the associated bivariate fractional derivative operators, derived by combining partial derivatives with the aforementioned fractional integrals. These operators give rise to a theory of two-dimensional fractional

We present an adaptation of a relatively simple topological argument to show the existence of many periodic orbits in an infinite dimensional dynamical system, provided that the system is close to a one-dimensional map in a certain sense. Namely, we prove a Sharkovskii-type theorem: if the system has a periodic orbit of basic period m, then it must have all periodic orbits of periods n⊳m, for n preceding

Combining the stabilized scalar auxiliary variable approach and the variable-step second-order backward difference formula, an adaptive time-stepping scheme is proposed for the two-mode phase-field crystal model with face-centered-cubic ordering. Specifically, introduce an auxiliary variable to handle the nonlinear term and obtain a new equivalent system, then perform a variable-step second-order approximation

Presume the uniform smooth Banach space E to possess p-uniform convexity for p≥2. In E, the VIP stands for a variational inequality problem and the CFPP a common fixed point problem of Bregman’s relative asymptotic nonexpansivity operator and finite Bregman’s relative demicontractions. We design and deliberate two adaptive double-inertial Bregman’s projection schemes with linesearch procedure for tackling

Accumulation operators play an important role in grey system models. However, with specific mechanism, each operator is effective only for specific temporal characteristics of the time series. In order to further utilize the effectiveness of existing accumulation operators, especially the ones with nonlinear features such as fractional order accumulation and information priority accumulation, this

In this work, we consider an inverse source problem for the time-space fractional diffusion equation with homogeneous Dirichlet boundary conditions, in which the spatial operator under consideration is the fractional Sturm–Liouville operator. We demonstrate that this inverse source problem is ill-posed in the sense of Hadamard and exhibit the uniqueness and conditional stability of its solution. To

In this paper, a third-order time adaptive algorithm with less computation, low complexity is provided for shale reservoir model based on coupled fluid flow with porous media flow. This algorithm combines a method of three-step linear time filters for simple post-processing and a second-order backward differential formula (BDF2), is third-order accurate in time, and provides no extra computational

We consider a two-dimensional sharp-interface model for solid-state dewetting of thin films with anisotropic surface energies on curved substrates, where the film/vapor interface and the substrate surface are represented by an evolving curve and a static curve, respectively. The continuum model is governed by the anisotropic surface diffusion for the evolving curve, with appropriate boundary conditions

To investigate the impact of the expanding region and harvesting pulses on population dynamics, we propose a one-dimensional logistic model that integrates harvesting pulses on a growing domain. By employing the eigenvalue method, we derive the explicit expression of the ecological reproduction index ℜ0 and analyze its pertinent properties. Subsequently, we explore the asymptotic behavior of solutions

In this paper, we analyze the unconditionally optimal error estimates of the linearized virtual element schemes for a class of nonlinear wave equations. For the general nonlinear term with non-global Lipschitz continuity, we consider a modified Crank–Nicolson scheme for the time discretization and a conforming virtual element method for the spatial discretization. Using the mathematical induction and

An accurate constitutive model for viscoelastic plates with variable thickness is crucial for understanding their deformation behaviour and optimizing the design of material-based devices. In this study, a variable order fractional model with a precise order function is proposed to effectively characterize the viscoelastic behaviour of variable thickness plates. The shifted Legendre polynomials algorithm

In this study, we introduce a phase field model designed to represent the intricate physical dynamics inherent in selective laser melting processes. Our approach employs a phase-field model to simulate the liquid–solid phase transitions, fluid flow, and thermal conductivity with precision. This model is founded on the variational principle, aiming to minimize the free energy functional, thereby guaranteeing

In this paper, we focus on the numerical approximation of the diffuse interface model for mass transfer through semi-permeable membranes which is proposed by using the energy variation method. A novel second-order fully decoupled and unconditionally energy stable scheme is constructed by introducing two types of nonlocal variables, one of which is to treat the nonlinear potential term, the other is

This paper is concerned with a class of non-linear uncertain differential equations driven by canonical process, which is the twin of Brownian motion in the structure of uncertain theory. By the Carathéodory approximation, we prove the existence and uniqueness of solutions for the considered equations under some non-Lipschitz conditions. Subsequently, By applying the chain rule for the considered equation

While the passivity of integer-order systems has been extensively analyzed, recent focus has shifted toward exploring the passivity of fractional-order systems. However, a clear definition of Nabla Fractional Order Systems (NFOSs) has not yet been established. In this work, the concepts of passivity, dissipativity, and finite-gain L2,α stability are extended to NFOSs, and relevant theories are proposed

The Wright–Fisher model is a useful SDE model, and it has many applications in finance and biology. However, it does not have an analytical solution currently. In this paper, we introduce a boundary preserving numerical method, called the projected EM method, to simulate it. We first use the projected EM method for the Lamperti transformed Wright–Fisher model. Then generated numerical solutions are

Discovering explicit governing equations of stochastic dynamical systems with both (Gaussian) Brownian noise and (non-Gaussian) Lévy noise from data is challenging due to the possible intricate functional forms and the inherent complexity of Lévy motion. This research endeavors to develop an evolutionary symbolic sparse regression (ESSR) approach to extract non-Gaussian stochastic dynamical systems

This paper explores the analysis and numerical solution of a fourth-order history-dependent hemivariational inequality. The variational formulation is derived from a model describing an elastic plate in contact with a reactive obstacle, where the contact condition involves both the subdifferential of a nonconvex, nonsmooth function and a Volterra-type integral term. We discretize the continuous formulation

An attempt has been made to understand the joint impact of predator induced fear and its carryover consequences with diffusion. The prey population such as European rabbit is captured and consumed by the predator, Iberian lynx. In the absence of diffusion, the system undergoes saddle–node and Hopf-bifurcation with respect to the carryover and fear parameters. Both the fear and carryover parameter affect

In this paper, a class of competitive neural network models based on octonions is first constructed, and its predefined-time synchronization is explored by applying non-separation method and aperiodic complete intermittent control. Based on classification analysis and measurable selection theory, two novel equalities regarding octonion algebra are developed, which play a key role in studying the synchronization

This paper establishes the conserved N-component Allen–Cahn model on evolving surfaces and conducts numerical simulations of the model. In mathematical modeling, since the surface motion velocity causes local contraction or expansion of the surface, it is hard to simultaneously fulfill the componential mass conservation and the point-wise mass conservation as the usual case on the static domain. Therefore

In this paper, by using the Lagrange multiplier approach and the operator splitting method, we construct some structure-preserving high-order and efficient compact difference schemes for nonlinear convection diffusion equations. For the one-dimensional model problem, we first introduce a high-order compact Strang splitting scheme (denoted as HOC-Splitting), which is fourth-order accurate in space and

Signal simplification is a processing technique that reduces the number of samples in a signal. It has been employed in various applications and methods while handling huge amounts of data. One well-known method is the Douglas-Peucker (DP) algorithm which performs signal simplification using an appropriate tolerance value to determine whether to retain or remove a given sample point. That would mean

This article explores the unsteady magnetohydrodynamic (MHD) model within the framework of porous media flow. This model consists of the Brinkman–Forchheimer equations and Maxwell equations in the porous media domain, which are coupled by the Lorentz force. We propose and analyze a numerical discretization method for MHD porous model. The second-order backward difference formula is utilized for temporal

Ray tracing through the crystalline lens of the eye is a complex optical problem traditionally tackled by mathematical techniques that may lack optimal accuracy. This paper introduces a novel method that integrates the Grey Wolf optimizer (GWO) with an artificial neural network (ANN), termed ANNGWO, to enhance the precision of ray tracing through the lens. The ANNGWO approach involves defining a cost

Two modified double inertial proximal point algorithms are proposed for solving variational inequality problems with a pseudomonotone vector field in the settings of a Hadamard manifold. Weak convergence of the proposed methods is attained without the requirement of Lipschitz continuity conditions. The convergence efficiency of the proposed algorithms is improved with the help of the double inertial

We study a first-passage time problem for a one-dimensional diffusion under stochastic resetting through a moving barrier described by a piecewise affine function. It is shown that the mean first-passage time can be minimized with respect to the resetting rate. However, the mean first-passage time exhibits multiple extrema as a function of the resetting rate, depending on the choice of the model parameters

Many problems in astrophysics cover multiple orders of magnitude in spatial and temporal scales. While simulating systems that experience rapid changes in these conditions, it is essential to adapt the (time-) step size to capture the behavior of the system during those rapid changes and use a less accurate time step at other, less demanding, moments. We encounter three problems with traditional methods

In this paper, the evolutionary exponential-polynomial-closure (EPC) method is extended to study the challenging problem of obtaining the evolutionary probability density function (EPDF) solutions of the nonlinear stochastic oscillators with one barrier under multiple modulated Gaussian white noise. Firstly, the original oscillator with the barrier is transformed into a new approximately equivalent

Saddle points are prevalent in complex systems and contain important information. The high-index saddle dynamics (HiSD) and the generalized HiSD (GHiSD) are two efficient approaches for determining saddle points of any index and for constructing the solution landscape. In this work, we first present an example to show that the orthonormality of directional vectors in saddle dynamics is critical in

This paper focuses on the hydrodynamically-coupled binary phase-field crystal (BPFC) model. Based on the L2-gradient flow, we derive the governing equations from the energy functional. To ensure the conservation of total mass, we incorporate two nonlocal Lagrange multipliers. For fluid dynamics, we employ the incompressible Navier–Stokes (NS) equations. Subsequently, we analytically prove the crucial

In this paper, we utilize the characteristic method to establish new sufficient conditions for the global exponential stability of periodic solutions for inertial delayed bidirectional associative memory (BAM) neural networks. The proposed criteria are presented as a series of linear scalar inequalities, which notably circumvent the use of the reduced order method and Lyapunov–Krasovskii functionals

In this paper, we investigate phase synchronization phenomena in weakly coupled oscillators, with a particular focus on the phase shifts that occur within Arnold tongues. Using a proposed theoretical approach, we provide proof of the existence of the corresponding cycle manifold near zero coupling, along with a detailed derivation of its shape. This allows us to explore the conditions under which phase-shift

This study encapsulates the multifaceted nature of attaining precise state tracking objectives in Markovian jump delay systems by encompassing a control technique related to delay compensation, fault tolerance, disturbance suppression and mismatch quantization. In brief, a quantized truncated predictive tracking control technique is implemented to achieve enhanced tracking outcomes by attenuating the

In this paper, observer-based aperiodic time-triggered intermittent control (OATIC) is introduced to study the exponential synchronization of chaotic Lur’e systems (CLSs). Firstly, the operation principle of CLSs with OATIC is elaborated in detail. Based on it, the mathematical expression of OATIC is proposed. Secondly, with the aid of the deduced lemma and the constructed mixed time-dependent Lyapunov

In this paper, we develop efficient implicit-explicit (IMEX) schemes for solving sixth-order Cahn–Hilliard-type equations based on the generalized scalar auxiliary variable (GSAV) approach. These novel schemes provide several remarkable advantages: (i) they are linear and only require solving one elliptic equation with constant coefficients at each time step; (ii) they are unconditionally energy stable

This paper concentrates on the synchronization problem of complex networks subject to coupling delays and impulsive disturbances, employing delayed state-feedback control strategies. By constructing a Lyapunov–Krasovskii functional with two different exponential decay rates, the complex networks with impulsive disturbances can achieve globally exponential synchronization (GES). Furthermore, the derived

In this work, an efficient fully discrete numerical scheme is presented for the Cahn–Hilliard–Navier–Stokes phase-field model. The combination of the variable time step second-order backward difference formula (VBDF2) and the finite element method is applied for discretization in time and space. Simultaneously, the scalar auxiliary variable (SAV) approach is employed to deal with the nonlinear term

In order to change the current situation where the numerical accuracy of existing fractional central difference (FCD) methods for integral fractional Laplacian (IFL) does not exceed second-order no matter how smooth the solution is. A simple and easy-to-implement high-order FCD scheme on uniform meshes is proposed for multi-dimensional IFL. The new generating functions are constructed to accommodate

In extreme flight environments, extreme oscillations may occur in aircraft seats, seriously endangering passengers’ comfort and safety. It is important to quantitatively study extreme events in the aircraft seats and control them. In this paper, a two-degree-of-freedom suspended seat is used to describe aircraft seats and a nonlinear energy sink (NES) is employed to suppress extreme events. The extreme

We consider third-order dynamic systems which have an integral feedback action and discontinuous relay disturbance. More specifically for the applications, the focus is on the integral plus state-feedback control of the motion systems with discontinuous Coulomb-type friction. We recall the stiction region is globally attractive where the resulting hybrid system has also solutions in Filippov sense

In this article, the stability problem for nonlinear systems and the synchronization of multilayered coupled quaternion networks involving memristor are separately discussed within a limited time, the time here can be determined by system or control parameters, or it can be specified by actual demand. To start with, based on exponential and hyperbolic cosine function, the theorems for limited-time

In this paper, a structure-preserving (for both ∇⋅uhn+1=0 and ∇⋅Bhn+1=0), unconditionally stable and decoupled scheme is proposed for the three-dimensional (3D) thermally coupled magnetohydrodynamic (MHD) model. Firstly, the thermally coupled MHD model is rewritten using the Lamb identity, and the variable vorticity is introduced to avoid ∇u existing. Secondly, the mixed finite element method is employed

We are concerned with the stabilization of nonlinear Timoshenko system just with local damping and local coupling effects, which come from the local memory/frictional terms and local coupling terms, acting on arbitrarily chosen subintervals. Especially, the subintervals do not necessarily include the ends and intersect each other, unlike what is usually required. For this challenging problem, we successfully

In this paper, a decentralized adaptive fuzzy fixed-time event-triggered control method is investigated for switched nonlinear interconnected systems (SNISs) under state-dependent switchings (SDSs). To deal with the problem that all the subsystems may be unstabilizable, the state-dependent switching method is introduced. The unknown nonlinear functions are approximated by interval type-2 fuzzy logic

The main objective of this article is to discuss the problem of finite-time stochastic input-to-state stability for a kind of stochastic delay continuous system with time-varying delay. By applying Lyapunov-Razumikhin functions as candidate functions, several sufficient criteria to ensure system stability are established. Different from the content of previous achievements, the event trigger switching

A vibration-driven locomotion robot, excited by periodic time-varying excitations has recently been studied and developed, which requires a complex controller. To simplify the control scheme, this article constructs a self-oscillation-driven locomotion in a liquid crystal elastomers (LCE)-based robot under constant illumination. This system consists of a robot's body and a self-oscillating LCE strip-spring

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

Thermodynamically consistent models in continuum physics, i.e. models which satisfy the first and second laws of thermodynamics, may be expressed using the metriplectic formalism. In this work, we leverage the structures underlying this modeling formalism to preserve thermodynamic consistency in discretizations of a fluid model. The procedure relies (1) on ensuring that the spatial semi-discretization

The evolution of complex dynamics in the second-order inverter with quasi-proportional integral resonance (PIR) controller is analyzed detailly in this paper, it is revealed that this inverter’s state changes not only from period-1 to chaos via period-doubling bifurcation, but also from stability to low-frequency oscillation via Hopf bifurcation, which will decrease the working life of the inverter

In this paper, an adaptive neural prescribed-time bipartite consensus tracking control scheme is investigated for nonlinear high-order multi-agent systems (HOMASs) with privacy preservation. Under the prescribed-time tracking control framework via the backstepping technique, among agents both cooperative and competitive relationships are considered. Moreover, a novel time-varying function is introduced

In this paper, we propose an efficient mesh-less method which combines the direct radial basis function partition of unity (D-RBF-PU) method and arbitrary Lagrangian–Eulerian (ALE) framework for solving parabolic PDEs on the evolving surface. The evolution mode of surface is obtained by the D-RBF-PU method for solving the forced mean curvature flow (FMCF). The new method maintains the quasi-uniformly

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