A challenging and common problem that frequently arises in the fields of physics and engineering, two-dimensional (2D) incompressible, viscous MHD duct flows have significant theoretical and practical significance due to their numerous and widespread applications in astrophysics, geology, power generation, MHD generators, electromagnetic pumps, accelerators, blood flow measurements, drug delivery,

Finite-time stability and explicit solutions are considered for nonhomogeneous fractional systems with pure delay. First, explicit solutions are obtained by using new delayed Mittag-Leffler-type matrix functions. Second, the finite-time stability results are obtained by utilizing these explicit solutions and the norm estimate of these delayed Mittag-Leffler-type matrix functions. The results improve

Variational Physics-Informed Neural Networks often suffer from poor convergence when using stochastic gradient-descent-based optimizers. By introducing a least squares solver for the weights of the last layer of the neural network, we improve the convergence of the loss during training in most practical scenarios. This work analyzes the computational cost of the resulting hybrid least-squares/gradient-descent

We present a full space-time numerical solution of the advection-diffusion equation using a continuous Galerkin finite element method on conforming meshes. The Galerkin/least-square method is employed to ensure stability of the discrete variational problem. In the full space-time formulation, time is considered another dimension, and the time derivative is interpreted as an additional advection term

This study investigates the dynamics of predator-prey interactions in both deterministic and stochastic environments, with a focus on the ecological implications of predator harvesting. Theoretical and numerical analyses explore local stability, bifurcations, and bionomic equilibria to identify sustainable harvesting strategies. Our findings reveal that increasing predator harvesting rates can induce

This article is concerned with constructing solutions involving nonlinear waves to a three-constant two-dimensional Riemann problem for a reduced hyperbolic model describing a thin film flow of a perfectly soluble anti-surfactant solution. Here, we solve the Riemann problem without the limitation that each jump of the initial data emanates exactly one planar elementary wave. We obtain ten topologically

In this contribution, we extend the hybridization framework for the Hodge Laplacian [Awanou et al. (2023) [16]] to port-Hamiltonian systems describing linear wave propagation phenomena. To this aim, a dual field mixed Galerkin discretization is introduced, in which one variable is approximated via conforming finite element spaces, whereas the second is completely local. The mixed formulation is then

Buchanan and Lillo both conjectured that oscillatory solutions of the first-order delay differential equation with positive feedback x′(t)=p(t)x(τ(t)), t≥0, where 0≤p(t)≤1, 0≤t−τ(t)≤2.75+ln⁡2,t∈R, are asymptotic to a shifted multiple of a unique periodic solution. This special solution can also be described from the more general perspective of the mixed feedback case (sign-changing p), thanks to its

This paper explores the consensus issue in second-order generalized nonlinear multiagent systems (MAS) that involve uncertain nonlinear dynamics and external disturbances from the system. Suppose that the uncertain nonlinear terms can be approximated by neural networks with nonlinear residues. Through the incorporation of localized adaptive observer and disturbance observer for each agent, we propose

Drawing on social learning theory, which emphasizes the dual influence of direct and indirect experience on behavior, this study extends the Spatial Prisoner's Dilemma game framework through three key innovations. First, we develop a link weight adjustment mechanism that incorporates tolerance, a previously neglected factor. Second, we extend the interaction probability model by integrating both direct

The current article focuses on the quasi-exponential stability analysis of non-autonomous integro-differential systems characterized by infinite delay. By developing a novel generalized Halanay inequality, sufficient conditions for the quasi-exponential stability of non-autonomous integro-differential systems with infinite delay are presented for the systems.

This paper considers a nonlocal reaction–diffusion model with a non-monotone birth pulse and a bistable response term. We define two monotone semiflows and, using the comparison argument, obtain the threshold dynamics between persistence and extinction in bounded domain. Moreover, we apply the asymptotic fixed point theorem to show the existence of bistable traveling wave solutions.

Indirect reciprocity, as a primary mechanism for cooperation between unrelated individuals, evaluates individuals' behavior and assigns reputation labels based on social norms. Since evaluating reputation is challenging in practice, unlike previous studies, we do not introduce the reputation evaluation rule but only record two recent action information as individuals' labels, including the most recent

The game of Showcase Showdown with unlimited spins is investigated as an n-players continuous game, and the Nash Equilibrium strategies for the players are obtained. The sequential game with information on the results of the previous players is studied, as well as three variants: no information, possibility of draw, and different modalities of winner payoff.

In this paper, we study an asymptotic preserving (AP), energy stable and positivity preserving semi-implicit finite volume scheme for the Euler-Poisson-Boltzmann (EPB) system in the quasineutral limit. The key to energy stability is the addition of appropriate stabilisation terms into the convective fluxes of mass and momenta, and the source term. The space-time fully-discrete scheme admits the positivity

This study develops a new family of explicit time integration methods for linear structural dynamic analysis. The proposed method is formulated using cubic B-spline interpolation. Several cases of algorithm parameters are identified by theoretical analysis to improve stability and accuracy. The explicit method exhibits desirable algorithmic properties, including stability and accuracy. The numerical

In this letter, we derive the sharp-interface limit of the Cahn–Hilliard–Biot equations using formal matched asymptotic expansions. We find that in each sub-domain, the quasi-static Biot equations are obtained with domain-specific material parameters. Moreover, across the interface, material displacement and pore pressure are continuous, while volumetric fluid content and normal stress are balanced

This paper proposes a physics-informed radial basis function network (RBFN) based on Hausdorff fractal distance to resolve Hausdorff derivative elliptic problems. In the proposed scheme, we improve the performance of RBFN via setting the source points outside the computational domain, and allocating distinct shape parameter values to each RBF. Furthermore, on the basis of the modified RBFN, we take

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 paper introduces a hybrid numerical method for simulating two- and three-dimensional nonlinear transient heat conduction problems with temperature-dependent thermal conductivity over extended time intervals. The approach employs the Krylov deferred correction method for temporal discretization, which is particularly effective for dynamic simulations requiring high accuracy. After temporal discretization

In this paper, the well-posedness and asymptotic behavior of a non-local lattice system are analyzed in the space ℓ1. In fact, the analysis is carried out in the subspace ℓ+1 formed by the nonnegative elements, remaining open the case of the whole space. The same problem has been analyzed recently in the space ℓ2 (see Y. Li et al., Communications on Pure and Applied Analysis, 23 (2024), 935-960). However

Exploring evolutionary updating rules more consistent with individual cognitive processes is crucial to the study of human cooperation. A considerable number of dynamic models describing human decision-making behavior lack empirical evidence. We have conducted a behavioral experiment and proposed a hypothesis that human players make decisions based on proportional change rather than absolute difference

This paper investigates the input-to-state stabilization (ISS) problem for nonlinear impulsive systems under event-triggered impulsive control (ETIC), encompassing comprehensive considerations of external continuous and impulsive disturbances. Some flexible design criteria of ETIC strategies are proposed for ISS of addressed systems based on Lyapunov theory without Zeno behavior, which can effectively

Due to the fact that higher-order interactions in neural networks significantly enhance the accuracy and depth of network modeling and analysis, this paper investigates the synchronization problem in such networks by employing a novel intermittent control method. Firstly, higher-order interactions in the fractional coupled neural network model are considered, extending the traditional understanding

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

This paper deals with a singular chemotaxis system with logistic source and non-sublinear production under homogeneous boundary condition: ut=Δu−χ∇⋅(uv∇v)+ru−μuk, vt=Δv−v+uβ in a bounded convex domain Ω⊂Rn with n≥1, here χ,μ>0, r∈R, k>1 and β≥1. It is proved that the system admits a global solution if k>2 with β∈[1,k−1), or k>1 and β≥1 with χ≤4nβ2. Moreover, the solution is globally bounded for the

In the current study, we propose an accurate numerical method for plane elastostatic equations of anisotropic functionally graded materials. The proposed method uses radial basis functions augmented with polynomial basis functions in a collocation framework by employing ghost point centers which cover physical domain of considered problem. Unlike in classical collocation approach where the centers

The laser-induced thermal therapy (LITT) scheme has proved great efficacy in tumor treatment. Therefore, the research between the heat conduction problems of LITT has become a hot topic in recent years. To seek rational constitutive relations of heat flux and temperature which can describe the heat transfer behavior of LITT, we develop a novel distributed-order time fractional derivative model based

We propose a scalable well-balanced numerical method to efficiently solve a modified set of shallow water equations targeting the dynamics of lava flows. The governing equations are an extension of a depth-integrated model already available in the literature and proposed to model lava flows. Here, we consider the presence of vents that act as point sources in the mass and energy equations. Starting

The recently proposed soft finite element method (SoftFEM) reduces the stiffness (condition numbers), consequently improving the overall approximation accuracy. The method subtracts a least-square term that penalizes the gradient jumps across mesh interfaces from the FEM stiffness bilinear form while maintaining the system's coercivity. Herein, we present two generalizations for SoftFEM that aim to

We develop a novel mixed method for addressing two-dimensional Laplacian problem with Dirichlet boundary conditions, which is recast as a rot-div system of three first-order equations. We have established the well-posedness of this new method and presented the a priori error estimates. The numerical applications of Bercovier-Engelman and Ruas test cases are developed, assessing the effectiveness of

In this paper, we develop a numerical method for determining the potential in one and two dimensional fractional Calderón problems with a single measurement. Finite difference scheme is employed to discretize the fractional Laplacian, and the parameter reconstruction is formulated into a variational problem based on Tikhonov regularization to obtain a stable and accurate solution. Conjugate gradient

As a continuation of Wang (2024), in the present paper, we consider the following problem in RN−Δu+V(x)u=λ(−ix⊥⋅∇u)+μu+|u|pu,u∈H1(RN,ℂ),∫RN|u|2dx=m>0,Re∫RN(−ix⊥⋅∇uu¯)dx=l∈R,where N=2 or N=3, x⊥ is the magnetic potential (see Introduction). When lm∉Z, 2

This paper is concerned with the spatial propagation of cooperative systems with general diffusions including multiple types of nonlocal dispersal mechanisms. We show the diversity of long-term behavioral patterns exhibited by different components within these systems, under the assumption that the diffusion operator bring about infinite spreading speed in propagation dynamics. Specifically, we observe

This note investigates the formation of singularities for the 3D Navier–Stokes equations. By employing a bilinear estimate and a logarithmic interpolation inequality, we derive a new extension criterion based on two vorticity components in Vishik-type spaces, which refines several previously established results concerning Navier–Stokes equations.

In this note we study the unsteady rectilinear flow of a fluid whose constitutive equation mimics that of a viscoplastic material. The constitutive relation is non-linear and is such that the stress cannot exceed a certain limit (limit stress fluid). The mathematical problem consists of the mass balance and the linear momentum equations as well as the initial and boundary conditions. We assume that

This article targets at addressing the controllability problem of a new introduced fractional-order impulsive and switching systems with time delay (FOISSTD). Toward this end, the algebraic method is adopted to establish the relevant controllability conditions. First, we obtain the solution representation of FOISSTD over every subinterval by resorting to the successive iterations and Laplace transform

Pest control is an important application of the Filippov system in ecology and has attracted much attention. Many studies on Filippov pest-natural enemy systems have been done by employing the widely recognized Integrated Pest Management (IPM) strategy. However, those studies primarily focused on planar Filippov models without considering the stage structure of populations. It is well-known that almost

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

In this study, using implicit Euler method and second-order centered difference methods to approximate the first-order temporal and second-order spatial derivatives, respectively, introducing a stabilized term and applying u(xi,yj,tk)−[u(xi,yj,tk)]pu(xi,yj,tk+1) to approximate the nonlinear term u(xi,yj,tk+1)−[u(xi,yj,tk+1)]p+1 at (xi,yj,tk+1), a class of stabilized, non-negativity- and boundedness-preserving

This paper is devoted to investigate a discrete Nicholson’s blowflies model with two delays. We construct some novel upper and lower solutions for the wave equation and then show the equation admits the traveling wave fronts connecting two equilibria of the associated spatially homogeneous system. And also, we obtain the non-existence for traveling waves of the model.

The W-random graphs provide a flexible framework for modeling large random networks. Using the Large Deviation Principle (LDP) for W-random graphs from [19], we prove the LDP for the corresponding class of random symmetric Hilbert-Schmidt integral operators. Our main result describes how the eigenvalues and the eigenspaces of the integral operator are affected by large deviations in the underlying