In this paper, a stochastic tumor–immune model with comprehensive pulsed therapy is established by taking stochastic perturbation and pulsed effect into account. Some properties of the model solutions are given in the form of the Theorems. Firstly, we obtain the equivalent solutions of the tumor–immune system by through three auxiliary equations, and prove the system solutions are existent, positive

In this work, we consider and analyze explicit exponential Runge–Kutta methods for solving semilinear time-fractional integro-differential equation, which involves two nonlocal terms in time. Firstly, the temporal Runge–Kutta discretizations follow the idea of exponential integrators. Subsequently, we utilize the spectral Galerkin method to introduce a fully discrete scheme. Then, we mainly focus on

This paper is mainly concerned with introducing a numerical method for solving initial–boundary value problems with integer and fractional order time derivatives. The method is based on discretizing the considered problems with respect to spatial and temporal domains. With the help of finite difference methods, we transformed the studied problem into a set of fractional differential equations. Then

In this article, based on the grad-div stabilization, we propose a generalized scalar auxiliary variable approach for solving a fluid–fluid interaction problem governed by the Navier–Stokes-/Navier–Stokes- equations. We adopt the backward Euler scheme and mixed finite element approximation for temporal-spatial discretization, and explicit treatment for the interface terms and nonlinear terms. The proposed

In this work, we present a conservative Allen–Cahn (CAC) equation and investigate its unconditionally maximum principle-preserving linear numerical scheme. The operator splitting strategy is adopted to split the CAC model into a conventional AC equation and a mass correction equation. The standard finite difference method is used to discretize the equations in space. In the first step, the temporal

An innovative simultaneous space–time Hermite wavelet method has been developed to solve weakly singular fractional-order nonlinear integro-partial differential equations in one and two dimensions with a focus whose solutions are intermittent in both space and time. The proposed method is based on multi-dimensional Hermite wavelets and the quasilinearization technique. The simultaneous space–time approach

In this paper, we employ the Lyapunov theory to generalize the finite time stability (FTS) results from general deterministic impulsive systems to impulsive stochastic time-varying systems, which overcomes inherent challenges. Sufficient conditions for the FTS of the system under stabilizing and destabilizing impulses are established by using the method of average dwell interval (ADT). For FTS of stabilizing

In this paper, we introduce a new sliding mode observer for Lur’e set-valued dynamical systems, particularly addressing challenges posed by uncertainties not within the standard range of observation. Traditionally, most ofLuenberger-like observers and sliding mode observer have been designed only for uncertainties in the range of observation. Central to our approach is the treatment of the uncertainty

The fractional material derivative appears as the fractional operator that governs the dynamics of the scaling limits of Lévy walks - a stochastic process that originates from the famous continuous-time random walks. It is usually defined as the Fourier–Laplace multiplier, therefore, it can be thought of as a pseudo-differential operator. In this paper, we show that there exists a local representation

Energy harvesters for mechanical vibrations are electro-mechanical systems designed to capture ambient dispersed kinetic energy, and to convert it into usable electrical power. The random nature of mechanical vibrations, combined with the intrinsic non-linearity of the harvester, implies that long, time domain Monte-Carlo simulations are required to assess the device performance, making the analysis

In this paper, a data-driven method is employed to investigate the probability density function (PDF) of nonlinear stochastic ship roll motion. The mathematical model of ship roll motion comprises a linear term with cubic damping and a nonlinear restoring moment represented as an odd-degree polynomial up to the fifth order. The data-driven method integrates maximum entropy, the pseudo-inverse algorithm

This paper addresses the input-to-state formation stabilization problem of nonlinear multi-agent systems within a hybrid impulsive framework, considering delay-dependent impulses, strong nonlinearity, and deception attack signals. By leveraging Lyapunov functionals, impulsive comparison theory, average impulsive interval methods, and graph theory, we develop novel criteria for possessing locally input-to-state

In the framework of perturbed Keplerian systems we deal with the Delaunay normalisation of a wide class of perturbations such that the radial distance is raised to an arbitrary real number . The averaged function is expressed in terms of the Gauss hypergeometric function whereas the associated generating function is the so called Appell hypergeometric function . The Gauss hypergeometric function related

Delayed resonator (DR), which enables complete vibration suppression through loop delay tuning, has been extensively investigated as a linear active dynamic vibration absorber since its invention. Besides, the nonlinear high-static-low-dynamic stiffness (HSLDS) has been widely used in vibration isolators for broadband (yet incomplete) vibration reduction. This work combines the benefits of DR and the

In the present study, we introduce a high-order non-polynomial spline method designed for non-linear time-fractional reaction–diffusion equations with an initial singularity. The method utilizes the L2-1 scheme on a graded mesh to approximate the Caputo fractional derivative and employs a parametric quintic spline for discretizing the spatial variable. Our approach successfully tackles the impact of

In this paper, we propose inertial Halpern-type algorithms involving a quasi-monotone operator for approximating solutions of variational inequality problems which are fixed points of quasi-nonexpansive mappings in reflexive Banach spaces. We use Bregman distance functions to enhance the efficiency of our algorithms and obtain strong convergence results, even in cases where the Lipschitz constant of

This paper delves into the synchronization dynamics of fractional-order memristor Cohen–Grossberg neural network systems with time-varying delays at predefined times (PTS-MFCGNNs). Firstly, leveraging the concept of predefined-time stability, we devise a fractional-order controller, establish sufficient conditions for predefined-time synchronization, and achieve synchronization within the Cohen–Grossberg

In this study, we investigate a control problem involving a reaction–diffusion partial differential equation (PDE). Specifically, the focus is on optimizing the chemotherapy scheduling for brain tumor treatment to minimize the remaining tumor cells post-chemotherapy. Our findings establish that a bang-bang increasing function is the unique solution, affirming the MTD scheduling as the optimal chemotherapy

The cell membrane has a layered structure, which separates the intracellular and extracellular ions for developing gradient electromagnetic field, and its flexible property enables the capacitance dependence on the shape deformation due to external stimuli. Therefore, piezoelectric membrane can be suitable to describe the biophysical characteristic of cell membrane and equivalent circuit approach becomes

To avoid solving a saddle-point system, in this paper, we study two-level Arrow–Hurwicz finite element methods for the steady bio-convection flows problem which is coupled by the steady Navier–Stokes equations and the steady advection–diffusion equation. Using the mini element to approximate the velocity, pressure, and the piecewise linear element to approximate the concentration, we use the linearized

The stochastic optimization of a nonlinear energy sink (NES) with a time-dependent stiffness is considered. The NES is linearly coupled to a main system. The optimization aims to find the stiffness properties of the NES that minimize the expected value of the velocity of the main system while accounting for the statistical distributions of the excitation amplitude and frequency. It is shown that the

This article addresses the challenge of achieving practically fast finite-time stabilization for stochastic constrained nonlinear systems, which are subject to both quantization effects and actuator dead zones. To tackle these issues, adaptive parameterization and partial control strategies are introduced with the aim of efficiently approximating and counteracting nonlinear disturbances. This approach

This paper investigates the problem of finite time prescribed performance control (PPC) for a number of nonlinear stochastic systems with asymmetric error constraint, unknown control directions, and actuator faults. Firstly, instead of introducing the performance constraint function in the Lyapunov function, a new asymmetric error conversion function (AECF) is presented, which can successfully constrain

Due to the existence of gaps or backlash, many mechanical systems can be simplified into piecewise linear models. The dynamic study on mechanical systems should be based on reliable mathematical models. So that it is very important to determine the contact point and separation point between the primary system and the auxiliary spring system (ASS) in a piecewise linear system. In most existing literature

In this article, we explore the general decay anti-synchronization (GDAS) and general decay anti-synchronization (GDHAS) of derivative coupled delayed memristive neural networks (DCDMNNs) with constant and delayed state coupling, respectively. To begin with, on account of the definitions of -type function as well as -type stability, we present the GDAS and GDHAS concepts for the considered DCDMNNs

In this article, a kind of second-order neural networks with variable coefficients and distributed delays are discussed. At first, new lemmas about fixed/preassigned-time synchronization for such system are respectively constructed. Then, some novel criteria are given to get fixed/preassigned-time synchronization for such delayed system based on the these lemmas. Unlike feedback controllers are used

This work presents an Ambrosetti–Prodi alternative for functional problems composed of a fully third-order differential equation with two types of functional boundary conditions. The discussion of existence and non-existence of solution is obtained in a more general case, and the multiplicity of solution is done with restrictive boundary conditions-

In this article, we propose a dynamic event-triggered neuro-optimal control scheme (DETNOC) for uncertain nonlinear systems subject to unknown dead-zone and disturbances through the design of a composite control law. An integral sliding mode-based discontinuous control law is utilized to compensate for the effects of unknown dead-zone, disturbance, and a component of uncertainties. As a result, a system

In this paper, we introduce some novel concepts within the realm of fuzzy bipolar metric spaces, namely ()-contractive type covariant mappings and contravariant mappings, and ()-contractive type covariant mappings. We establish some fixed point theorems that demonstrate both the existence and uniqueness of fixed points for ()-contractive type covariant mappings and contravariant mappings, and for ()-contractive

In this paper, we investigate the control and dynamic behavior of the inverted pendulum system with time delay under fractional Gaussian noise excitation. For H=1/2 and H, we analyze the stochastic dynamic characteristics of the system under Hopf bifurcation, utilizing time delay and noise intensity as bifurcation parameters, and validate the theoretical conclusions through numerical simulations. We

This paper considers a Belousov–Zhabotinskii reaction–diffusion system with spatio-temporal delay. The spatio-temporal delay is modeled as the convolution of with a kernel function , where . By constructing an auxiliary system, applying Schauder’s fixed point theorem, and using a limiting argument, we demonstrate that the model admits non-negative traveling wave solutions connecting the equilibrium

In this paper, we deal with numerical approximations for solving the Black–Scholes Partial Differential Equation (PDE) for European and American options pricing with local volatility. This PDE is well-known to be degenerated. Local volatility model is a model where the volatility depends locally of both stock price and time. In contrast to constant volatility or time-dependent volatility models for

– In this paper, we consider the following stationary two-species chemotaxis-competition system with signal-dependent diffusion and sensitivity in a bounded smooth domain , where are positive constants, and with for all . Since there does not exist an immediate change variable that transforms (0.1) into a semilinear system when (0.1) is considered with being arbitrary functions in , this makes the

Discrete grey forecasting models based on an accumulative operator have been widely used in many practical fields. With the development of grey forecasting models, it is a problem to be solved to further analyze internal mechanisms and unify the structures. This paper aims to reconstruct the model from a perspective of sequence characteristics and simplify the modeling steps under the condition of

As we all know, the output of a system is affected by its input and response properties. When the input switches, there must exist a transient process in the output and this transient process is different for different systems due to their different response properties and different dynamic process. However, the response property and dynamic process have rarely been studied in the obtained achievements

This paper investigates the problem of secure synchronization in aperiodic intermittent event-triggered pinning control for discrete-time complex networks (DCNs) against multi-pattern link attacks. Firstly, in order to reduce communication burden and control cost, a novel aperiodic intermittent event-triggered control (AIEC) with discontinuous characteristics is designed based on periodic sampling

The correlation between convergence deformation and the safety state of a cross-jointed segmental lining is investigated and clarified. The limitations of convergence deformation as a measuring scale is explored also. Firstly, an analytical algorithm (known as the relative stiffness method, RSM) is developed and verified for tracing the mechanical response of a cross-jointed segmental lining in failure

Self-oscillating motion have the capacity to autonomously converting ambient power into repetitive motion without requiring an additional control unit, and designing more self-oscillating can broaden their utilization in energy extraction, robotic systems, and sensors. However, cyclic self-oscillating motions often cause structural instability and increase friction. To address these challenges, we

This article discusses the deformation of semiconductor cylinders in the context of photothermoelastic theory. The proposed model is used to describe thermal waves, plasma waves, and elastic waves and analyze the theoretical analysis of thermal deformation effects on semiconductor hollow cylinders. The interior of the hollow cylinder is clamped and unaffected by thermal loads and carrier concentrations

A two-dimensional multiterm fractional delay diffusion equation is considered. The representation of the exact solution of the equation is derived and it is shown that the solution exhibits singular behaviors at multiple nodes due to the initial singularity and time delay. This results in the numerical schemes for solving the equation typically have a lower order of convergence in time. The problem

In this work, we introduce an innovative fractional nonlinear parabolic model using a time-fractional order derivative, specifically employing the sense for fractional differentiation. This model aims to enhance traditional super-resolution models, particularly in the context of multi-frame image super-resolution. Additionally, we incorporate a regularized Perona–Malik diffusion mechanism to control

Novel multi-step predictor–corrector numerical schemes have been derived for approximating decoupled forward–backward stochastic differential equations. The stability and high order rate of convergence of the proposed schemes are rigorously proved. We also present a sufficient and necessary condition for the stability of the schemes. Numerical experiments are given to illustrate the stability and convergence

This paper presents a nonlinear reaction–diffusion-fluid system that simulates radiofrequency ablation within cardiac tissue. The model conveys the dynamic evolution of temperature and electric potential in both the fluid and solid regions, along with the evolution of velocity within the solid region. By formulating the system that describes the phenomena across the entire domain, encompassing both

In this paper, we present a comprehensive study of the fingering phenomenon of a power-law non-Newtonian fluid falling down a cylinder surface. A theoretical analysis is firstly carried out and the governing equation describing the film thickness is established for the non-Newtonian fluid denoted by a power-law index . Using the lubrication theory with dimensionless variables, the partial differential

This paper introduces a modified bilinear model for integer-valued time series in which thinning operators are applied in bilinear terms involving the product of the input and state process separately. The proposed model is able to consider overdispersion. Furthermore, it connects a feature of the integer-valued autoregressive conditional heteroskedasticity and integer-valued autoregressive processes

We analyze a periodically-forced dynamical system inspired by the SIR model with impulsive vaccination. We fully characterize its dynamics according to the proportion of vaccinated individuals and the time between doses. If the is less than 1 (), then we obtain precise conditions for the existence and global stability of a disease-free solution. Otherwise, if , then a globally stable solution emerges

The vector-valued Allen–Cahn equations have been extensively applied to simulate the multiphase flow models. In this paper, we consider the maximum bound principle (MBP) and corresponding numerical schemes for the vector-valued Allen–Cahn equations. We firstly formulate the stabilized equations via utilizing the linear stabilization technique, and then focus on the bounding constant of the nonlinear

Influence maximization problem (IM) has been extensively applied in fields such as viral marketing, rumor control, and infectious disease prevention. However, research on the IM problem has primarily focused on ordinary networks, with limited attention devoted to hypergraphs. Firstly, we propose an efficient evaluation method, i.e., the multiple-hop probability dissemination method (MHPD), aiming to

We consider the classical approximation of a realistic model for the scattering of He atoms from Cu surfaces. For this problem, modeled by a two-degrees-of-freedom Hamiltonian system, the existence of chaos has been proven analytically very recently for sufficiently large values of the energy, if some quantity, known as the Stokes constant, is non-zero (Borondo et al., 2024). Taking two different and

This paper continues to explore the membrane potential reconstruction and pattern recognition problem in a neural tissue modeled by Stochastic Dynamic Neural Field (SDNF) equation. Although recent research has suggested an efficient solution based on the state-space approach through nonlinear Bayesian filtering framework, it is becoming extremely difficult to ignore the existence of non-Gaussian uncertainties

In this paper, we focus on the numerical simulation for two-dimensional nonlinear fractional sub-diffusion equations in the presence of time delay. Firstly, we investigate the existence, uniqueness and regularity of the solution for such problems. The theoretical result implies that the solution at is smoother than that at , where is a constant time delay, and this is an improvement for the work (Tan

This paper mainly explores the fixed-time and preassigned-time output synchronization of spatiotemporal networks with directed topology. Firstly, a kind of exponential-type control scheme associated with output feedback is developed. Subsequently, several sufficient criteria are established to ensure fixed-time output synchronization by utilizing the Lyapunov method and Taylor expansion. Moreover,

Due to the irreversibility of processes in an enclosed system, the randomness in the system increases in time and can be represented by an accumulated noise stochastic process. In contrast to the thermodynamics theory, the analysis of the system is based on the information theory point of view. The system is defined by two states: a time state and a timeless state. Based on the central limit theorem

This paper focuses particularly on the influence of wedge duration on spiral wave formation and the regulation of electromagnetic noise. The motion stability or periodicity of a constructed regular neuronal network system is revealed by applying the master stability function method. The effect of wedge duration and electromagnetic noise on spiral wave dynamics is quantified using defined metrics, and

In this paper, we propose a new mathematical model to investigate nosocomial infections caused by both antibiotic-sensitive and antibiotic-resistant bacteria. A focus of our modeling study is the presence of multiple transmission pathways, including the primary infection, co-infection, and re-infection from each type of bacteria, and their interplay with each other in the process of disease spread

In this paper, we study a first-order Euler semi-implicit finite element scheme for the two-dimensional incompressible Boussinesq equations for magnetohydrodynamics convection with the temperature-dependent viscosity, electrical conductivity and thermal diffusivity. In finite element discretizations, the mini finite element is used to approximate the velocity and pressure, and the piecewise linear

A two point boundary value problem for a singularly perturbed system with double root of the degenerate equation is studied. This is a new class of problem in the case when the nonlinear term at the right end of the system is discontinuous on the straight line, which leads to the formation of complex multizonal internal layers that can be divided into eight regions in the neighborhood of the discontinuous

In this research we aim to estimate three parameters in a stochastic generalized logistic differential equation. We assume the intrinsic growth rate and shape parameters are constant but unknown. To estimate these two parameters, we use the maximum likelihood method and establish that the estimators for these two parameters are strongly consistent. We estimate the diffusion parameter by using the quadratic

In this paper, we consider a first-order projection finite element scheme for the three dimensional incompressible magnetohydrodynamics system based on a magnetic vector potential formulation by writing the magnetic induction , where is a magnetic potential. The main advantage of this projection scheme has two-fold. One is that numerical solutions of velocity field and magnetic induction both satisfy

The effects of contact stiffness between the rotor and stator on the internal resonance of forward and backward whirls in the rotating frame have been investigated, that is the forward and backward modes are commensurate in the rotating frame. First, the equations for an overhung rotor system with two rotors with coupling stiffness are established by Lagrangian method. By the transformation of a general