The paper is devoted to the discrete Lyapunov equation X − A * X A = C , where A and C are given operators in a Hilbert space H and X should be found. We derive norm estimates for solutions of that equation in the case of unstabl...
In this paper, we consider the numerical solution of large-scale discrete-time projected Lyapunov equations. We provide some reasonable extensions of the most frequently used low-rank iterative methods for linear matrix equations, such as the low-ran...
The paper studies numerical methods that preserve a Lyapunov function of a dynamical system, i.e., numerical approximations whose energy decreases, just like in the original differential equation. With this aim, a discrete gradient method is implemen...
We present a comprehensive mathematical analysis of a within-host dual-target HIV dynamics model, which explicitly incorporates the virus’s interactions with its two primary cellular targets: CD4+ T cells and macrophages. The model is formulate...
Due to its significance in numerous scientific and engineering domains, discrete fractional calculus (DFC) has received much attention recently. In particular, it seems that the exploration of the stability of DFC is crucial. A mathematical model of...
The aim of this work is to describe the dynamics of a discrete fractional-order reaction–diffusion FitzHugh–Nagumo model. We established acceptable requirements for the local asymptotic stability of the system’s unique equilibrium....
This paper introduces the Fourier spectral method combined with the strongly stable exponential time difference method as an attractive and easy-to-implement alternative for the integration of the multi-dimensional Allen–Cahn equation with no-flux bo...
In this paper, we study various variants of Verhulst-like ordinary differential equations (ODE) and ordinary difference equations (O Δ E). Usually Verhulst ODE serves as an example of a deterministic system and discrete logistic equation is...
This work studies certain perturbed and un-perturbed nonlinear systems of continuous and discrete integro-delay differential equations (IDDEs). Using the Lyapunov–Krasovskii functional (LKF) method and the Lyapunov–Razumikhin method (LRM)...
In this paper, a family of temporal high-order accurate numerical schemes for the Landau–Lifshitz–Gilbert (LLG) equation is proposed. The proposed schemes are developed utilizing the Gauss–Legendre quadrature method, enabling them t...
In this paper, applying some properties of matrix inequality and Schur complement, we give new upper and lower bounds of the solution for the unified algebraic Lyapunov equation that generalize the forms of discrete and continuous Lyapunov matrix equ...
Lyapunov equations are key mathematical objects in systems theory, analysis and design of control systems, and in many applications, including balanced realization algorithms, procedures for reduced order models, Newton methods for algebraic Riccati...
A numerical scheme is said to be locally exact if after linearization (around any point) it becomes exact. In this paper, we begin with a short review on exact and locally exact integrators for ordinary differential equations. Then, we extend our app...
In this survey, we have included the recent results on Lyapunov-type inequalities for differential equations of fractional order associated with Dirichlet, nonlocal, multi-point, anti-periodic, and discrete boundary conditions. Our results involve a...
In this paper, we consider nonlinear integration techniques, based on direct Padé approximation of the differential equation solution, and their application to conservative chaotic initial value problems. The properties of discrete maps obtain...
In this research paper, we solve the problem of synchronization and anti-synchronization of chaotic systems described by discrete and time-delayed variable fractional-order differential equations. To guarantee the synchronization and anti-synchroniza...
This work is concerned with the delay-dependent criteria for exponential stability analysis of neutral differential equation with a more generally interval-distributed and discrete time-varying delays. By using a novel Lyapunov–Krasovkii functi...
Dynamical systems described by fractional-order difference equations have only been recently introduced inthe literature. Referring to chaotic phenomena, the type of the so-called “self-excited attractors” has been so far highlighted amon...
We investigate the solvability and stability properties of a class of nonlinear stochastic delay differential equations (SDDEs) driven by Wiener noise and incorporating discrete time delays. The equations are formulated within a Banach space of conti...
This express brief deals with the problem of the state variables regulation in the ball and beam system by applying the discrete-inverse optimal control approach. The ball and beam system model is defined by a set of four-order nonlinear differential...
This paper primarily focuses on the chaos synchronisation analysis of neural networks (NNs) under a hybrid controller. Firstly, we design a suitable hybrid controller with saturated impulse control, combined with time-dependent intermittent control....
This contribution concerns the development of generic methods and tools for robust optimal control of high-pressure liquid chromatographic separation processes. The proposed methodology exploits a deterministic robust formulation, that employs a line...
This study applies reinforcement learning to search parameter regimes that yield chaotic dynamics across six systems: the Logistic map, the Hénon map, the Lorenz system, Chua’s circuit, the Lorenz–Haken model, and a custom 5D hyper...
Differential equations have demonstrated significant practical effectiveness across diverse fields, including physics, chemistry, biological engineering, computer science, electrical power systems, and security cryptography. This study investigates t...
Using fractional difference equations to describe fractional and variable-order maps, this manuscript discusses the dynamics of the discrete 4D sinusoidal feedback sine iterative chaotic map with infinite collapse (ICMIC) modulation map (SF-SIMM) wit...
This paper focuses on high performance adaptive robust position control of electro-hydraulic servo system. The main feature of the paper is the combination of adaptive robust algorithm with discrete disturbance estimation to cope with the parametric...
Robust stability/stabilization for discrete-time time-varying Markovian jump linear systems subject to block-diagonal stochastic parameter perturbations is addressed in this paper. Using a scaling technique, we succeed in effectively addressing the m...
We propose a generalized multiscale finite element method combined with a balanced truncation to solve a parameter-dependent parabolic problem. As an updated version of the standard multiscale method, the generalized multiscale method contains the ne...
The present study focuses on the dynamical aspects of a discrete-time Leslie-Gower predator-prey model accompanied by a Holling type III functional response. Discretization is conducted by applying a piecewise constant argument method of differential...
In this paper, we discuss stochastic differential-algebraic equations (SDAEs) and the asymptotic stability assessment for such systems via Lyapunov exponents (LEs). We focus on index-1 SDAEs and their reformulation as ordinary stochastic differential...
The stability of bilinear systems is investigated using spectral techniques such as selective modal analysis. Predictive models of bilinear systems based on inductive knowledge extracted by big data mining techniques are applied with associative sear...
We consider the problems of state feedback and static output feedback preview controller (PC) for uncertain discrete-time multiple-input multiple output (MIMO) systems based on the parameter-dependent Lyapunov function and the linear matrix inequalit...
A nonlinear mathematical model of COVID-19 containing asymptomatic as well as symptomatic classes of infected individuals is considered and examined in the current paper. The largest eigenvalue of the next-generation matrix known as the reproductive...
Based on the two-dimensional reaction–diffusion model, the spatiotemporal dynamical characteristics of the semi-discrete pine–Monochamus alternatus system with cross-diffusion and convection effect were studied in this work. Firstly, the...
This paper provides a useful supplement note for implementing the Kalman filters. The material presented in this work points out several significant highlights with emphasis on performance evaluation and consistency validation between the discrete Ka...
This research focuses on the development of state-difference feedback controllers for discrete-time (DT) nonlinear descriptor systems. Discrete-time nonlinear DA systems consist of difference and algebraic equations and play a crucial role in describ...
This paper investigates the possibilities of complex nonlinear dynamic signal generation using a simple photorefractive two-wave mixing system without any feedback using numerical simulations. The novel idea is to apply a sinusoidal electric field to...
This paper introduces a novel model order reduction (MOR) method for linear discrete-time systems, focusing on frequency-limited balanced truncation (BT) techniques. By leveraging Laguerre functions, we develop two efficient MOR algorithms that avoid...
The limit of validity of ordinary statistical mechanics and the pertinence of Tsallis statistics beyond it is explained considering the most probable evolution of complex systems processes. To this purpose we employ a dissipative Landau–Ginzbur...
This paper proposes a dynamical approach to determine the optimal values of the parameters used in each iteration of the symmetric successive over-relaxation (SSOR), accelerated over-relaxation (AOR), and symmetric accelerated over-relaxation (SAOR)...
This work is devoted to the modeling and investigation of the architecture design for the delayed recurrent neural network, based on the delayed differential equations. The usage of discrete and distributed delays makes it possible to model the calcu...
In this article, a new competitive neural network (CNN) with reaction-diffusion terms and mixed delays is proposed. Because this network system contains reaction-diffusion terms, it belongs to a partial differential system, which is different from th...
This paper presents a new third-order symmetric difference equation transformed into a 3D discrete symmetric map. The nonlinear dynamics and symmetry of the proposed map are analyzed with two initial conditions for exploring the sensitivity of the ma...
This research study investigates the issue of finite-time passivity analysis of neutral-type neural networks with mixed time-varying delays. The time-varying delays are distributed, discrete and neutral in that the upper bounds for the delays are ava...
The present study investigates non-fragile H∞ state estimation based on a dynamic event-triggered mechanism for a class of discrete time-varying nonlinear systems subject to dynamical bias and fading measurements. The dynamic deviation caused b...
The problem of tomographic image reconstruction can be reduced to an optimization problem of finding unknown pixel values subject to minimizing the difference between the measured and forward projections. Iterative image reconstruction algorithms pro...
The stability of energy demand–supply systems is often affected by delayed feedback caused by regulatory inertia, communication lags, and heterogeneous agent responses. Conventional models typically assume discrete delays, which may oversimplif...
The aim of this paper is to investigate the qualitative behavior of a mathematical model of the COVID-19 pandemic. The constructed SAIRS-type mathematical model is based on nonlinear delay differential equations. The discrete-time delay is introduced...
We develop and analyze a distributed-delay model for nutrient–fish–mussel dynamics in multitrophic aquaculture systems. Extending the classical discrete-delay framework, we incorporate gamma-distributed kernels to capture the time-distrib...
This study addresses the nonlinear forced vibration of a functionally graded (FG) nanobeam subjected to mechanical impact and electromagnetic actuation. Two symmetrical actuators were present in the mechanical model, and their mechanical behaviors we...
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