Uncertainty quantification is of great significance to enhance the reliability and robustness of flexible multibody systems. The Polynomial chaos-Legendre metamodel (PCLM) method is commonly employed for hybrid uncertainty analysis of multibody systems; however, the fitting accuracy deteriorates over time when dealing with periodic time domain problems. To solve this problem, the Polynomial chaos-Legendre

The Koopman operator approach provides a powerful linear description of nonlinear dynamical systems in terms of the evolution of observables. While the operator is typically infinite-dimensional, it is crucial to develop finite-dimensional approximation methods and characterize the related approximation errors with upper bounds, preferably expressed in the uniform norm. In this paper, we depart from

One of the oldest methods for computing invariants of ordinary differential equations is tested using the full Toda lattice model. We show that the standard method of undetermined coefficients and modern symbolic algebra tools together with sufficient computing power allow to compute Darboux invariants without any additional information.

Mean field games equations are examined for conservation laws. The system of mean field games equations consists of two partial differential equations: the Hamilton–Jacobi–Bellman equation for the value function and the forward Kolmogorov equation for the probability density. For separable Hamiltonians, this system has a variational structure, i.e., the equations of the system are Euler–Lagrange equations

In real traffic networks, route choice preferences tend to prioritize the shortest travel time over the shortest distance. To address this, we propose a cascading failure model that incorporates time dynamics. By introducing the BPR function, our model quantifies edge transmission time, identifies time-optimal paths, and distributes loads proportionally based on edge time weights. Three parameters

In this paper, we propose a fixed-time neurodynamic optimization algorithm with time-varying coefficients (TFxND) for solving split equality problems. Under bounded linear regularity condition, we prove that the proposed neurodynamic algorithm converges to a solution of the split equality problem in fixed-time, which is independent of the initial states. In addition, the proposed TFxND is applied to

In this paper, a linearized fully discrete scheme is proposed to solve the two-dimensional nonlinear time fractional Schrödinger equation with weakly singular solutions, which is constructed by using L1 scheme for Caputo fractional derivative, backward formula for the approximation of nonlinear term and five-point difference scheme in space. We rigorously prove the unconditional stability and pointwise-in-time

In this paper, several energy-conserving numerical schemes are constructed for solving the two-dimensional Maxwell equations. Initially, the original problem is decomposed into two one-dimensional subproblems using operator splitting techniques. Subsequently, for spatial discretization, we employ the local radial basis function (LRBF) method, while for temporal discretization, three different splitting

We present a new robust and decoupled scheme for Biot’s model with displacement-dependent nonlinear permeability. The scheme combines a low-order H(div)-conforming element pair P1⊕RT0−P1 approximation with a first-order semi-explicit time discretization. Two stabilization terms are incorporated into the modified conforming-like formulation to achieve the scheme’s stability. One term penalizes the nonconformity

This paper addresses the growing concern of stability analysis and controller design in Markovian jumping conic-type nonlinear systems, particularly in light of their increasing applications in various fields such as the optimization and motor device control systems, making the understanding of time-varying delays crucial. Utilizing variable-period mode-dependent sampled-data control, an augmented

A dual-triggered adaptive neural control scheme for a class of multiple-input multiple-output (MIMO) switched nonlinear cyber–physical systems under dual-channel deception attack is proposed in this paper. The dual-triggered mechanism for both sensor-to-controller and controller-to-actuator channels within the traditional backstepping framework is designed to effectively reduce the communication and

This article investigates the problem of H∞ filtering for Takagi–Sugeno (T–S) fuzzy systems under denial-of-service (DoS) attacks. A new dynamic event-triggered mechanism (DETM) combined with DoS attack is proposed, which can dynamically optimize the trigger parameters in accordance with the change of external output. This mechanism can successfully transmit the most recent measurement output to the

The main purpose of this paper is to propose and analyze two accelerated subgradient extragradient methods with increasing self-adaptive step size for solving pseudomonotone variational inequality problems in Hilbert spaces. Under some appropriate conditions imposed on the parameters, we combine the inertial subgradient extragradient method with viscosity and Mann-type iterative methods, respectively

It is necessary to have an accurate nonlinear dynamic model for purpose of design of optimization of systems constructed by pneumatic artificial muscles (PAM) based on McKibben structure. Hence, this paper will develop an accurate dynamic model of PAM. As known, PAM tube is made of the rubber and it is also reinforced by metal fibers wrapping around the tube. In order to study comprehensively, the

In this work, the nonlinear flutter characteristics of the truncated porous sandwich conical shell with variable stiffness under simply supported boundary, which is placed in the thermal environment and supersonic flow, are explored. The sandwich variable stiffness conical shell is constructed of two carbon fiber surface sheets and a porous core with aluminum foam, which has the exponential variable

This paper proposes a command filter approximator-based fixed-time fuzzy control (CFTFC) method for n-dimensional nonlinear systems subject to function uncertainties, input saturation, and external disturbances. Command filter approximators are designed to provide differential estimations for the jth (j=1,2,…,n−1) subsystem of the error system, addressing both function uncertainties and the complex

In this article, the synchronization issue of Markovian neural networks with reaction–diffusion phenomena (RDMNNs) in complex noise environments is studied. Firstly, Lévy noise is incorporated into the model as the stochastic noise source for the system, and the impact of different noise intensities on the stability of the error system is analyzed. Furthermore, the dynamic changes in system parameters

Synchronization dynamics is a phenomenon of great interest in many fields of science. One of the most important fields is neuron dynamics, as synchronization in certain regions of the brain is related to some of the most common mental illnesses. To study the impact of the network heterogeneity in the neuronal synchronization, we analyze a small-world network of non-identical Chialvo neurons that are

In this paper, the optimal fault tolerant control problem is investigated for constrained multiplayer systems with external disturbances and completely unknown dynamics. According to games theory, each control player along with its corresponding fault player and disturbance player can be regarded as a two-player zero-sum game, respectively. To release the restriction on the system dynamics, a neural

Fractals are a common geometric structure in nature, exhibiting the rich complexity and regularity of the physical world. In the study of complex networks, the self-similarity and multi-layered characteristics of fractal networks make them an ideal model for investigating information dissemination mechanisms. This paper constructs a fractal social network with three-layer granularity structure and

In this paper, we discuss set differential systems with control effects and non-instantaneous impulses. A generalized Cauchy–Schwarz inequality is first proposed. The stability criteria of such systems based on our proposed inequality and Lyapunov function method are obtained. Moreover, the hybrid controller including a set-valued feedback controller and a non-instantaneous impulsive controller is

We introduce two extragradient methods that incorporate one-step inertial terms and self-adaptive step sizes for equilibrium problems in real Hilbert spaces. These methods synergistically combine inertial techniques and relaxation parameters to enhance convergence speed while ensuring superior performance in addressing pseudomonotone and Lipschitz continuous equilibrium problems. The first method is

This study investigates the mechanism of temporary capture about the Moon, either originating from periodic orbits or following bounce-back trajectories associated with the libration point dynamics of the Sun–Earth system. The primary objective is to analyze the maneuvers required for temporary capture and to explore possibilities for natural temporary capture in the Earth–Moon system. We begin by

The present paper is concerned with the analysis of a nonlinear 3D model in mechanics of deformable solids whose material law is represented by an implicit subdifferential inclusion governed by a bipotential. In this context, we draw attention to a particular class of bipotentials by introducing the notion of g- bipotential. The weak formulation of the model under consideration leads to a variational

This paper presents an in-depth analysis of numerical methods for solving two-dimensional fractional time–space stochastic diffusion equations, employing the Caputo fractional derivative and the fractional Laplacian. The study utilizes the L1-algorithm for temporal discretization, ensuring an accurate representation of fractional dynamics, while the Fast Fourier Transform is applied for spatial discretization

In this paper, we investigate the linear vibration behaviors, nonlinear and chaotic dynamics of the functionally graded graphene reinforced titanium-based (FG-GRTB) composite laminated cantilever rectangular plate under the transverse excitation. Based on Halpin-Tsai model, the mechanical properties are calculated for the graphene reinforced titanium-based (GR-TB) composite laminated cantilever rectangular

Self-sustainable systems can absorb energy from steady environment and spontaneously generate continuous motions. Inspired by explosive predation of the mantis shrimp, this paper designs a self-striking hammer using liquid crystal elastomers (LCEs) powered by steady illumination, which consists of an LCE fiber, a rope, a slider, a track, two springs, and a hammer. The mechanical model of the self-striking

The Saltzman–Sutera model is a simplified system of ordinary differential equations that captures the essential dynamics of Earth’s glacial cycles over the past two million years. Despite its simplicity, the model accounts for significant climate phenomena. In this paper, we rigorously investigate the integrability and dynamics of the Saltzman–Sutera model. (i) First, we demonstrate the non-existence

Identification of stiff nonlinear systems is considered as one of the challenging tasks and research community is providing promising solution for identification of these systems. Researchers have concluded that integration of fractional calculus provides better insight and understanding of complex systems by keeping the previous history. In this study, nonlinear marine predator optimization algorithm

Comprehensive studies that fully explore the impact of tooth surface morphology on the time-varying mesh stiffness (TVMS) of helical gear pairs are limited. The slicing method in helical gears leads to significant differences in fractal contact stiffness compared to spur gears, affecting stiffness calculations. Consequently, this research focuses on super-high-contact-ratio (SHCR) helical gears, commonly

The path tracking control of unmanned vehicles in complex driving conditions is frequently challenged by the model uncertainty and the external disturbance, such as the crosswind disturbance, which brings difficulties to the path tracking control. Therefore, to address the path tracking control of unmanned vehicles under complex driving conditions, a composite anti-disturbance path tracking control

In recent years, the effects of heredity on dynamical systems have been analysed using the fractional derivative. But, another way of considering the heredity is the integral formulation

Inverse optimal control is a framework to deal with the optimal control of dynamical systems with uncertain parameters. Bioconversion of glycerol to 1,3-propanediol in continuous fermentation is a complex cellular metabolic process in nature. Due to the unclear metabolic mechanisms and the lack of experimental data of intracellular concentrations, kinetic parameters of the fermentation system are often

This paper provides a sufficient criterion for robust global exponential stability (RGES) of non-deterministic fuzzy neural networks (NDFNNs), where “non-deterministic” feature maps the effect of the variability of piecewise constant argument (PCAs), derivative term coefficients (DTCs) and twofold uncertain connection weights.To determine the supremum of the non-deterministic parameters, an algorithm

In this paper, we study the relationship between occupation and closeness of nodes for particles moving in a random walk on weighted complex networks, such that the adjacency and transition matrices define the outgoing neighbors of a node and transition probabilities to them, respectively, for packages that pass through the node in question. To answer this question for different network topologies

A general method is presented to study the bifurcations that occur in models of anomalous φ0 Josephson junctions. To demonstrate the method, a bifurcation analysis is made of the superconductor–ferromagnet–superconductor φ0 Josephson junction, in which the Josephson to magnetic energy ratio and the direct current bias are used as the two control parameters. The recently developed embedding technique

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

The Glansdorff and Prigogine General Evolution Criterion (GEC) is an inequality that holds for macroscopic physical systems obeying local equilibrium and that are constrained under time-independent boundary conditions. The latter, however, may prove overly restrictive for many applications involving fluid flow in physics, chemistry and biology. We therefore analyze in detail a physically more-encompassing

To extend the discrete velocity method (DVM) and unified methods to more realistic boundary conditions, a Cercignani–Lampis (CL) boundary with different momentum and thermal energy accommodations is proposed and integrated into the DVM framework. By giving the macroscopic flux from the numerical quadrature of the incident molecular distribution, the reflected macroscopic flux can be obtained for the

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