The research focuses on relative controllability of neutral delay differential equations on quaternion skew field (NDQDEs). First, we derive the representation of solutions for NDQDEs by quaternion determining equations and neutral delay quaternion matrix function. Then, the Gram criterion of relative controllability for NDQDEs in different cases is given with the help of the representation of solutions

In this paper, some novel stochastic finite time stability (SFTS) criteria are derived for impulsive switched stochastic nonlinear systems (ISSNS) by using stochastic process theory, multiple Lyapunov functions, analytical techniques. Moreover, the estimations of stochastic settling time (SST) are also provided. Under the influence of destabilizing and stabilizing impulses, we consider situations where

The multi-stable vibrational systems have attracted widespread attention due to their rich nonlinear dynamic phenomena. This study constructs a tristable nonlinear energy sink with time-varying potential barriers (VP-TNES) for the first time, aimed at enhancing vibration suppression efficiency of traditional TNES. The VP-TNES builds time-varying potential barriers with symmetrical magnetic oscillators

The normal functioning of the actual brain relies on the collaborative efforts of neurons across multiple functional regions as well as the support and regulation of astrocytes, and its operating environment is both intricate and diverse. Hence, to replicate the electrophysiological properties of the central nervous system more accurately, it is essential to take the neuronal heterogeneity, the role

In response to the failure problem of axial-torsional coupling vibration of drill string in oil & gas wells, an axial-torsional coupling nonlinear vibration model of drill string is established using the finite element method, which can effectively simulate the coupling vibration of actual wellbore drill string multi-body systems and the real-time rock breaking effect. Moreover, the correctness and

This study presents a novel event-triggered joint adaptive high-gain observer design for delayed output-sampled nonlinear systems with output injection. These systems are characterized by the presence of unknown parameters that influence both the state and output equations. The major difficulty in designing the observer lies in the interplay between event-triggered mechanism, output injection, and

We present an extragradient-type algorithm for solving a nonmonotone and non-Lipschitzian equilibrium problem over the fixed point set of a nonexpansive mapping in a Hilbert space. We obtain that the sequence generated by the presented algorithm converges weakly to a solution of the problem. The weak convergence does not require any monotonicity and Lipschitz continuity of the involved equilibrium

The inverse eigenvalue problem of weighted Helmholtz equations is investigated. The density function is recovered from the observation of the limited spectral data. It is reformulated as an optimization problem and a multi-objective loss function is defined accordingly. A multi-artificial neural network (multi-ANN) algorithm is proposed. The existence and stability of the solution of the optimization

In this work we focus in the family of real planar polynomial vector fields of arbitrary degree. We are interested in to characterize when a (local) center singularity of these vector fields becomes a global center, that is, its period annulus foliates the punctured real plane. The characterization of any global center is done by blowing-down the polycycle at infinity into a monodromic singular point

In this paper, the finite-time synchronization (FTS) problem of fractional-order multiplex networks with internal delay, intra- and inter-layer coupling delays, and uncertain intra- and inter-layer coupling matrices is studied. A new hybrid controller, composed of an impulsive controller and a quantized controller, is designed to achieve FTS for the considered network in order to save control resources

We consider a Froeschlé map and we add a weak dissipation proportional to ɛ3, where ɛ is the parameter of perturbation. We compute formal expansions of lower dimensional tori, both in the conservative and weakly dissipatives cases, and use them to estimate the shape of their domains of analyticity with respect to ɛ. Our results support conjectures in the literature.

There are already several methods to calculate the time-varying minimal rank outer inverse (TV-MROI), but few scholars have employed fixed-time methods to obtain TV-MROI. To obtain TV-MROI within a fixed time frame, this paper introduces four novel fixed-time zeroing neural network (ZNN) models specifically designed to solve the TV-MROI problem. Compared with existing ZNN models, the proposed fixed-time

In this article, the fixed-/predefined-time stability (FXTS/PTS) problems of impulsive fuzzy neural networks are concerned. Under the framework of Filippov solution, some more comprehensive FXTS/PTS theorems of discontinuous impulsive systems are first established by employing the Lyapunov method. Compared to most existing results, which require the Lyapunov function (LF) to be negative or semi-negative

This paper explores two-dimensional flows near a free critical point in an incompressible viscoelastic Maxwell medium, governed by a rheological constitutive law. While stagnation point flow problems have been widely studied, general exact analytical solutions for stresses in cylindrical coordinates - more practical and suitable for certain experiments—remain undiscovered. In this study, we derive

Motivated by the practical interest in the third-body perturbation as a natural cleaning mechanism for high-altitude Earth orbits, we investigate the dynamics stemming from the secular Hamiltonian associated with the lunar perturbation, assuming that the Moon lies on the ecliptic plane. The secular Hamiltonian defined in that way is characterized by two timescales. We compare the location and stability

The work is dedicated to exploring nonlinear modal interactions and mechanisms of energy transfer between a linear oscillator and a nonlinear energy sink in the gravitational field. Nonlinear modal interactions are studied based on the frequency-energy plot. Periodic motions are computed via numerical continuation method. Numerical evidences reveal that a 1:1 in-phase oscillation exists at low energies

In this work the authors present a new class of radial basis functions (RBF) using functions from the κ-generalized Kaniadakis thermostatistics and the Lambert–Kaniadakis Wκ function, a recent generalization of the Lambert W function using the κ-exponential. Such functions are used to build neural networks of radial basis functions (RBFN). Two applications of these new RBFNs are described: In the first

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

This work is mainly concerned with small noise and small time asymptotics for a class of McKean–Vlasov stochastic differential equations with local Lipschitz coefficients. We apply the modified weak convergence criteria to prove the Laplace principle (equivalently, the large deviation principle). The main results extend the existing ones to the case of fully local assumptions with respect to both the

The paper is concerned with a new class of differential hemivariational inequalities which appears as the weak formulation of steady thermistor problems with mixed boundary conditions. First, we show the existence of solution to this kind of inequality problems combining the theory of pseudomonotone operators and a fixed point argument. Then, an optimal control problem is considered where the control

We study the dynamics of compacton light beams in a weakly nonlocal nonlinear medium with concurrent nonlocality. This study, which is analytical and numerical, focuses on the propagation, stability and interaction of these optical beams. We show that in the absence of diffraction, compacton beams propagate in a stable manner. When diffraction is taken into account, the dynamics of the propagation

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

Studying the intrinsic mechanisms of coupled information and epidemic transmission can enhance public understanding of the dynamic processes involved in epidemic transmission. Heterogeneous individual activity levels reshape propagation mechanisms, influencing the co-evolutionary dynamics of information and epidemics. We developed a novel coupled information-epidemic model to investigate how variations

This study seeks to achieve exponential stabilization of uncertain Takagi–Sugeno (T–S) fuzzy systems with stochastic time-varying delays using a switching event-triggered H∞ control strategy. A delay decomposition scheme is used to build a time-dependent piecewise Lyapunov function and stability criteria are established using reciprocally convex and integral inequalities. A switched event-triggered

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

This is a comprehensive study on a 2-degree-of-freedom flutter-based aeroelastic piezoelectric energy harvester supported with cubic and quintic nonlinear springs under unsteady airflow. The nonlinear system is simplified by dimension reduction analysis for a high-dimensional multistable system, and the flutter envelope is predicted and the parameters studied to analyze the effect on linear critical

Change points in real-world systems mark significant regime shifts in system dynamics, possibly triggered by exogenous or endogenous factors. These points define regimes for the time evolution of the system and are crucial for understanding transitions in financial, economic, social, environmental, and technological contexts. Building upon the Bayesian approach introduced in Adams and MacKay (2007)

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

We study a single-species chemostat model with variable nutrient input and variable dilution rate with delayed (fixed) response in growth. The first goal of this article is to prove that persistence implies uniform persistence. Then we concentrate on the particular case with periodic nutrient input and same periodic dilution with delayed response in growth. We obtain a threshold that allows us to determine

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