The main goal of this paper is to investigate the multi-parameter stability result for a stochastic fractional differential variational inequality with Lévy jump (SFDVI with Lévy jump) under some mild conditions. We verify that Mosco convergence of the perturbed set implies point convergence of the projection onto the Hilbert space consisting of special stochastic processes whose range is the perturbed

The joined effects of syntrophic relationship and substrate inhibition are considered in a diffusive model of the anaerobic digestion process. We first establish the existence and structure of coexistence solutions for the system in different growth rate parameter ranges. Numerical results suggest that the coexistence solutions of the system undergo double bifurcation in the suitable range of growth

In modern engineering practice, there is a steady increase in the need for multi-dimensional global approximations of complex black-box functions involved in today's engineering design problems. Metamodels have been proved to be effective alternatives for analyzing and predicting highly complex original models at a lower computational cost. The Kriging model is valued for its ability to predict the

Classical spectral methods are confined to numerically solving Fredholm integro-differential equations in regular domains, such as rectangles and discs. This paper aims to numerically address two-dimensional Fredholm integro-differential equations in complex geometries by combining spectral methods with mapping techniques. Initially, we transform the computational domain into a rectangular one via

Fractional-order derivative-based modeling is crucial for describing real-world forecasting problems and analyzing proposed models. It provides an advanced framework for examining intricate variations in various systems, enhancing understanding and analysis. We present a new fractional order nonlinear model for dynamics and forecasting of nitrogen oxides (NOx) and ozone (O3) in the atmosphere, crucial

Systemic risks do not arise only as a result of a crisis event, and it is important to understand the ex-ante risk contagion mechanisms. There has been no research on ex-ante contagion valuation and contagion modeling of multilayer networks. This study proposes the ex-ante-contagion mechanism of a two-layer network financial system with interbank lending connections and cross-holding connections, constructs

This paper introduces balanced implicit two-step Maruyama methods for solving Itô stochastic differential equations. Such methods, compared to those corresponding standard linear two-step Maruyama methods, have better mean-square properties, which is confirmed by a comparison of the stability regions for some particular two-step Maruyama methods. Moreover, the convergence order is investigated which

Linear and nonlinear vibration absorbers are employed to achieve rapid and effective suppression of the induced vibration into structural dynamical systems to protect their structural integrity and to avoid human and economic losses. The majority of considered high performance vibration absorbers in the literature are still not capable to achieve complete vibration suppression during the first cycle

In this paper, a novel type of fractional complex networks with unbounded coupling delays (FCNUCD) is investigated. The adaptive feedback control strategy is proposed to achieve the leader-following synchronization of the FCNUCD. The leaderless synchronization of the FCNUCD is also achieved by employing the edge-based adaptive control strategy. Furthermore, a new mixed adjustment rule is proposed in

A significant limitation of conventional risk theory models in insurance is the explicit assumption that different lines of insurance business operations are uncorrelated. This paper addresses this limitation by introducing a novel multivariate size-dependent renewal risk model. The authors adopt a t-copula-based approach to model dependence structures between different types of claims, allowing for

Nonlinear energy sinks (NESs) have received widespread attention due to their broadband vibration absorption ability. This study investigates the vibration suppression of a double-cable beam structure by NES. Firstly, a mechanical model of the double cable-beam-NES structure was established, and the Hamilton principle was used to derive the motion partial differential equation of the double cable-beam-NES

In this paper, the issue of tracking control for nonlinear systems under external disturbances and asymmetric states-time-related full-state constraints imposed dynamically is studied. An adaptive fuzzy command filtered control method is developed. Firstly, the nonlinear nonstrict feedback system subjected to unknown disturbances and dynamic full-state constraints is modeled. Then, a fuzzy state observer

Nowadays, pipelines are often used in marine engineering to effectively transport oil and natural gas due to their good continuity and high efficiency. However, the unwanted dynamics of the pipelines caused by the interaction between the external environment and internal fluid pipelines may affect their normal operation and service life. In the paper, we present a fiber-reinforced composite pipeline

The goal of this paper is to study an abstract system of nonlinear differential hemivariational inequality, which consists of nonlinear differential inclusions and evolutionary hemivariational inequalities with doubly nonlinear function. The differential inclusion is also driver by time dependent maximal monotone operators with nonlinear perturbations. Firstly, the discrete iterative problems are constructed

Deterministic growth laws, expressed by first order differential equations with time-depending intrinsic growth intensity function, are initially introduced. Such equations are then parameterized in a way to allow random fluctuations of the intrinsic growth intensity function. This procedure leads to time-inhomogeneous diffusion processes for which a detailed study of transition probability density

Image inpainting is a technique that utilizes information from surrounding areas to restore damaged or missing parts. To achieve binary image inpainting with mathematical tools and numerical techniques, an effective mathematical model and an efficient, stable numerical solver are essential. This work aims to propose a practical and unconditionally stable numerical algorithm for image inpainting. A

We study controllability and observability concepts of tempered fractional linear systems in the Caputo sense. First, we formulate a solution for the class of tempered systems under investigation by means of the Laplace transform method. Then, we derive necessary and sufficient conditions for the controllability, as well as for the observability, in terms of the Gramian controllability matrix and the

In this paper, we propose a partially degenerated weighted network dynamical model for dengue fever transmission to study its spatial transmission dynamics, in which population mobility are characterized by the weighted graph Laplacian diffusion. Firstly, we establish the comparison principle for general reaction–diffusion differential equations defined on finite weighted network. Next, the well-posedness

In this study, we utilize Gaussian Mixture Model (GMM) and propose a novel learn algorithm to approximate any density in a fast and simple way. In our previous study, we proposed a idea called GMM expansion which inspired by Fourier expansion. Similar to the base of frequencies in Fourier expansion, GMM expansion assume that normal distributions can be placed evenly along the support as a set of bases

This paper addresses the numerical implementation of the transparent boundary condition (TBC) and its various approximations for the free Schrödinger equation on a rectangular computational domain. In particular, we consider the exact TBC and its spatially local approximation under high frequency assumption along with an appropriate corner condition. For the spatial discretization, we use a Legendre–Galerkin

We consider a generic Susceptible–Infected–Recovered–Hospitalized–Deceased model for the spread of infectious diseases over contact networks. Precisely, the deceased compartment tracks the cumulative number of deaths that are not offset by births. After properly reducing the model to a nonlinear susceptible–infected–recovered (SIR) model on a graph, we systematically investigate its invariant sets

In this paper, we provide a rigorous proof of the convergence for both first-order and second-order exponential time differencing (ETD) schemes applied to the nonlocal Cahn–Hilliard (NCH) equation. The spatial discretization is executed through the Fourier spectral collocation method, whereas the temporal discretization is implemented using ETD-based multistep schemes. The absence of a higher-order

This paper focuses on the finite/fixed time synchronization (FFTS) issue for heterogeneous-coupled complex dynamic networks (CDNs) with random perturbations and time delay. A new adaptive control algorithm with quantization and update law is proposed, and FFTS can be realized by a unified controller. Combined with Lyapunov functions and stability theory, the finite/fixed time stochastic synchronization

This paper investigates the periodic attitude motion of a gyrostat spacecraft in weakly elliptical orbits, focusing on the derivation of approximate analytical solutions and their stability. Unlike circular orbits, which allow for three types of regular precession, elliptical orbits are limited to cylindrical precession. Notably, the research identifies stable periodic attitude motions with the period

Dispersion entropy (DisEn), as the advanced entropy metric for measuring signal complexity, still suffers from inevitable deficiencies in dynamic estimation accuracy due to the neglect of differences within patterns. To address the problem, the extended dispersion entropy (EDisEn) is proposed, which considers the differences within the patterns to extend the dispersion patterns by utilizing the cosine

This paper explores adaptive neural fault-tolerant control for nonlinear systems characterized by a nonstrict-feedback structure, tackling the difficulties arising from unmodeled dynamics and unknown backlash-like hysteresis. A dynamic signal is introduced to mitigate the adverse effects of unmodeled dynamics, while radial basis function neural networks (RBFNNs) are utilized to capture the unknown

This article presents a novel computational algorithm for solving the fractional pantograph differential equation (FPDE). The algorithm is based on introducing a new family of orthogonal polynomials, generalizing the second-kind Chebyshev polynomials family. Specifically, we use the shifted generalized Chebyshev polynomials of the second kind (SGCPs) as basis functions, approximating the solutions

This paper mainly focuses on the steady-state bifurcation at the interior positive constant steady state of a diffusive Leslie–Gower model with both-density-dependent fear effect. Taking the growth rate of the predator as the bifurcation parameter and using Crandall–Rabinowitz bifurcation theorem, we discuss the local and the global steady-state bifurcation near the homogeneous steady state, and analyze

This paper addresses Exponential input-to-state stability (EISS) for coupled Van der Pol system under the second-order process is researched. Sufficient criterion for EISS is obtained through graph theory, Kirchhoff’s matrix-tree theorem and many stochastic processes knowledge. Eventually, an instance of a heart is given to explain the result and the meaning of the study.

The main objective of this paper is to design an aperiodically intermittent control to ensure the finite and fixed time synchronization of fuzzy cellular neural networks (FCNNs) involving switching parameters with threshold properties, time-dependent discrete, continuous-type delays, and stochastic disturbances during transmission. Cellular neural networks (CNNs), with their grid-like structure, excel

This paper studies the Hopf bifurcation and transitions of firing activities in a fractional-order FitzHugh-Rinzel system with multiple time delays. We first explicitly derive the stability condition of the system without delays and the fractional-order-induced Hopf bifurcation distinguishes between resting and firing. When unstable, there exist complex oscillations, including spiking, mixed-mode oscillations

Combustion occurring in porous media has various practical applications, such as in in-situ combustion processes in oil reservoirs, the combustion of biogas in sanitary landfills, and many others. A porous medium where combustion takes place can consist of layers with different physical properties. This study demonstrates that the initial value problem for a combustion model in a multi-layer porous

The phase field model is a popular mathematical tool for studying tumor growth. It describes the tumor growth via marking the tumor area. Since skin tumors are usually accompanied by the raised growth of skin tumor area, such as the keloid, the simulation is requested to simultaneously mark the tumor area and the height of the skin bulge. This paper combines the phase field model with the evolving

We use the statistical properties of Shannon entropy estimator and Kullback–Leibler divergence to study the predictability of ultra-high frequency financial data. We develop a statistical test for the predictability of a sequence based on empirical frequencies. We show that the degree of randomness grows with the increase of aggregation level in transaction time. We also find that predictable days

Many real-world decision problems can be naturally modeled as fractional optimal parameter selection and fractional optimal control problems. Therefore, in this paper, we consider a class of combined fractional optimal parameter selection and optimal control problems involving nonlinear fractional systems with Caputo fractional derivatives and subject to canonical equality and inequality constraints

This research investigates the impact of radiation pressure, albedo effect, and oblateness in the generalized Circular Restricted Three-Body Problem (CR3BP). We have considered the bigger primary is a radiating primary and the smaller primary produces the albedo effect. Moreover, the smaller primary is also considered as oblate body with zonal harmonic coefficient Ji;i=2,4. In this study, we have computed

In this paper, we present and study two new two-step inertial accelerated algorithms for finding an approximate solution of split feasibility problems with multiple output sets. Our methods are extensions of CQ algorithms previously studied in the literature. In contrast to the related iterative methods for solving SFP, our methods incorporate a two-step inertial technique that speeds up the convergence

Angular misalignment error is a prevalent occurrence in gear systems, mainly caused by manufacturing and installation errors in gearbox components. This significantly impacts the meshing characteristics of the system, making it necessary to carry out the nonlinear dynamic analysis of spur gear pairs with angular misalignment errors. In this study, a meshing stiffness model for a spur gear pair with

Starting from a 4 × 4 matrix Sylvester equation, the matrix mKdV system as an unreduced equation is worked out and the explicit expression of its solution is presented by applying the Cauchy matrix method. Then, two kinds of reduction conditions are given, under which the complex three-component mKdV(CTC-mKdV) equation and the real three-component mKdV(RTC-mKdV) equation can be obtained, and finally

Phase separation, the formation of two distinct phases from a single homogeneous mixture, has been extensively studied and observed in classical systems, typically as temperature changes. These separation phenomena depend on temperature and vary with different materials. We explore the numerical model, which shows various aspects of phase separation, such as time delay, the influence of heterogeneous

This paper is concerned with the distributed fixed-time neural network adaptive tracking control issue for heterogeneous vehicular platoon suffered from actuator faults. Due to the string instability of vehicles caused by non-zero initial spacing errors (ISEs), an improved exponential spacing policy is proposed to eliminate the influence of non-zero ISEs by introducing a compensated term, while guaranteeing

A new procedure for the construction of higher-dimensional Lie–Hamilton systems is proposed. This method is based on techniques belonging to the representation theory of Lie algebras and their realization by vector fields. The notion of intrinsic Lie–Hamilton system is defined, and a sufficiency criterion for this property given. Novel four-dimensional Lie–Hamilton systems arising from the fundamental

In this work, the binary mixture of nematic liquid crystals and viscous fluids (NLC-VF) system consists of the Cahn–Hilliard (CH) equations for the phase-field variable for the free interface, the Allen–Cahn (AC) type constitutive equation for the nematic director, and the incompressible Navier–Stokes (NS) equation for the two fluids. To address the computational challenges posed by this complex system

This paper concerns a backward Euler stabilizer-free weak Galerkin finite element method (SFWG-FEM) for the time-dependent Poisson–Nernst–Planck (TD-PNP) problem. The scheme we propose utilizes spaces Pk(K), Pk(e), [Pj(K)]2 to approximate the interior, edge, and discrete weak gradient spaces on each element K and edge e⊂∂K, respectively. The proposed method is in a simple format similar to the regular

Physics-informed neural networks are a powerful deep-learning framework that integrates physical laws to solve partial differential equations, yet achieving fast convergence and high prediction accuracy remains challenging due to the ongoing issue of obtaining high-quality training data. In this study, we introduce a sampling-enhanced framework to unify residual-based sampling methods of PINNs. To

In this paper, we consider resistance distances in stretched Cantor product networks, a family of non-self-similar networks. By constructing the networks in a iterated way, we give an approach to encode every node in their vertex set. And then we simplify the complex resistor networks by induction on the basic network pattern. Using classical results of circuit theory, we obtain the exact formulae

In this paper, we investigate the existence of solutions for double-phase problems with variable exponents of the Kirchhoff–Schrödinger type, incorporating a convection term. By imposing certain assumptions and utilizing the topological degree for a class of (S+)-demicontinuous operators, along with the Galerkin method within the framework of Musielak–Orlicz–Sobolev spaces, we establish the existence

The main aim of this paper is to propose a 2-step backward differential formula (BDF2) fully discrete scheme with the bilinear Q11 finite element method (FEM) for the nonlinear reaction–diffusion equation. By use of the combination technique of the element’s interpolation and Ritz projection, and through the interpolation post-processing approach, the superclose and global superconvergence estimates

We study the global bifurcation diagram and corresponding global phase portraits in the Poincaré disc for a generalized van der Pol-Duffing oscillator, which has four nonlinear terms with arbitrary orders. This nonlinear oscillator possesses more diverse and complicated dynamical behaviours, including the heteroclinic bifurcation, generalized Hopf bifurcation and pitchfork bifurcation. Moreover, theoretical

Considered herein is the initial–boundary value problem for a fractional pseudo-parabolic equation with memory term and logarithmic nonlinearity given by ut+(−Δ)su+(−Δ)sut=∫0tg(t−τ)(−Δ)su(τ)dτ+uln|u| under different initial energy levels. The local well-posedness of weak solution is firstly established by using Galerkin approximation and contraction mapping principle at arbitrary initial energy level

In this paper, we derive an effective 1D equation based on the work of Mateo and Delgado [Phys. Rev. A 77, 013617 (2008)] that governs the axial dynamics of mean-field cigar-shaped Bose–Einstein condensates (BECs) with repulsive interatomic interactions and subject to transverse anti-Gaussian confining potential. The resulting equation exhibits a nonstandard nonlinearity written in terms of the principal

This paper investigates the problem of fault diagnosis and fault-tolerant control in switched systems with actuator fault under unknown input disturbances. Initially, an adaptive unknown input observer capable of rapidly estimating faults was designed, incorporating proportional terms to enhance the response speed of fault estimation. Subsequently, by employing the average dwell time approach and using

Personal audio systems have been studied extensively since their inception nearly three decades ago. Acoustic Contrast Control (ACC) method is extensively employed due to its capability to establish a distinct contrast in acoustic energy between bright and dark zones. But it fails to ensure a uniform sound field distribution within the bright zone, potentially compromising the auditory comfort experienced

A linearized decoupled fully discrete scheme is developed and investigated for the coupled nonlinear semiconductor device problem with low order nonconforming EQ1rot element. Then, by use of its special property: the consistency error in the broken H1-norm can reach to second order when the exact solutions belong to H3(Ω), just one order higher than its interpolation error, together with some proper

This paper considers consumer-resource systems, where the consumer moves on a fully-connected patch network and behaves like an agent. Using graph-theoretical method and dynamical systems theory, we show global equilibrium stability in the system. Analysis on the equilibrium demonstrates that when the dispersal rate is small, the effect of network topology is the result of the effect of each path in

This study delves into exploring dissipative synchronization for a class of switched neural networks with external disturbances featuring reaction–diffusion terms under the master–slave scheme. Precisely, the addressed network model comprises a hybrid attack model which entails both deception and denial-of-service attacks. Moreover, security-based control is designed to achieve the intended results

In this study, we extend the Morris-Lecar (M-L) neuron model to design a neuronal network model with field effects. Using Lyapunov theory and the master stability function to evaluate the stability of synchronous manifolds. The Hamilton energy function of a single neuron is derived using Helmholtz's theorem to equivalently describe its internal field energy, and bioelectric activities are analyzed

In this paper, authors present a memristor-based fractional order system of tri-diagonal bidirectional associative memory neural networks (TdBAMNNs) incorporating leakage and communication delays. The existence and uniqueness theorem is established for the memristor-based fractional-order TdBAMNNs system. Analysis of Hopf bifurcation anti-control is conducted using various feedback controllers by exploring

It is well known that Newton’s method can have trouble converging if the initial guess is too far from the solution. Such a problem particularly occurs when this method is used to solve nonlinear elliptic partial differential equations (PDEs) discretized via finite differences. This work focuses on accelerating Newton’s method convergence in this context. We seek to construct a mapping from the parameters

In this paper, the exponential synchronization problem for fractional-order T–S fuzzy complex multi-links networks under an intermittent dynamic event-triggered control (IDE-TC) strategy is discussed. To this end, a new triggering rule with a dynamical variable is first introduced, including some available static triggering rules as its particular form. Then, it is proved that the applied dynamical