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Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^\alpha x(t)=\delta…

Dynamical Systems · Mathematics 2022-08-29 Sachin Bhalekar , Deepa Gupta

We analyze the stability of standing pulse solutions of a neural network integro-differential equation. The network consists of a coarse-grained layer of neurons synaptically connected by lateral inhibition with a non-saturating nonlinear…

Neurons and Cognition · Quantitative Biology 2007-05-23 Yixin Guo , Carson C. Chow

This paper is concerned with the numerical approximation of stochastic ordinary differential equations, which satisfy a global monotonicity condition. This condition includes several equations with super-linearly growing drift and diffusion…

Numerical Analysis · Mathematics 2015-10-09 Wolf-Jürgen Beyn , Elena Isaak , Raphael Kruse

In this paper, We study the stability of solutions of fuzzy differential equations by Lyapunov's second method. By using scale equations and comparison principle for Lyapunov - like functions, we give some sufficient criterias for the…

Dynamical Systems · Mathematics 2007-05-23 Le Van Hien

Strong stability preserving (SSP) methods are designed primarily for time integration of nonlinear hyperbolic PDEs, for which the permissible SSP step size varies from one step to the next. We develop the first SSP linear multistep methods…

Numerical Analysis · Mathematics 2022-04-05 Yiannis Hadjimichael , David Ketcheson , Lajos Lóczi , Adrián Németh

A nonlinear stochastic differential equation with the order of nonlinearity higher than one, with several discrete and distributed delays and time varying coefficients is considered. It is shown that the sufficient conditions for…

Probability · Mathematics 2018-10-25 Leonid Shaikhet

A new criterion for A-stability of peer two-step methods is presented which is verifiable exactly in exact arithmetic by checking semi-definiteness of a certain test matrix. It depends on the existence of two positive definite weight…

Numerical Analysis · Mathematics 2015-06-19 Bernhard A. Schmitt

This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…

Probability · Mathematics 2023-05-22 Taras Lukashiv , Igor V. Malyk , Maryna Chepeleva , Petr V. Nazarov

In this paper, the problem of stability in terms of two measures is considered for a class of stochastic partial differential delay equations with switching. Sufficient conditions for stability in terms of two measures are obtained based on…

Dynamical Systems · Mathematics 2016-09-07 Shufen Zhao , Minghui Song

The input/output stability of an interconnected system composed of an ordinary differential equation and a damped string equation is studied. Issued from the literature on time-delay systems, an exact stability result is firstly derived…

Optimization and Control · Mathematics 2018-09-24 Matthieu Barreau , Frédéric Gouaisbaut , Alexandre Seuret , Rifat Sipahi

Fractional order differential and difference equations are used to model systems with memory. Variable order fractional equations are proposed to model systems where the memory changes in time. We investigate stability conditions for linear…

Dynamical Systems · Mathematics 2025-02-12 Prashant M. Gade , Sachin Bhalekar , Janardhan Chevala

We provide explicit conditions for uniform stability, global asymptotic stability and uniform exponential stability for dynamic equations with a single delay and a nonnegative coefficient. Some examples on nonstandard time scales are also…

Dynamical Systems · Mathematics 2019-02-21 Elena Braverman , Basak Karpuz

For simulating large networks of neurons Hines proposed a method which uses extensively the structure of the arising systems of ordinary differential equations in order to obtain an efficient implementation. The original method requires…

Numerical Analysis · Mathematics 2017-03-27 Michael Hanke

It is well-known that wave-type equations with memory, under appropriate assumptions on the memory kernel, are uniformly exponentially stable. On the other hand, time delay effects may destroy this behavior. Here, we consider the…

Analysis of PDEs · Mathematics 2015-07-14 Cristina Pignotti

High-order spatial discretizations with strong stability properties (such as monotonicity) are desirable for the solution of hyperbolic PDEs. Methods may be compared in terms of the strong stability preserving (SSP) time-step. We prove an…

Numerical Analysis · Mathematics 2014-01-30 Christopher Bresten , Sigal Gottlieb , Zachary Grant , Daniel Higgs , David I. Ketcheson , Adrian Németh

Based on a regularized Volterra equation, two different approaches for numerical differentiation are considered. The first approach consists of solving a regularized Volterra equation while the second approach is based on solving a…

Numerical Analysis · Mathematics 2007-12-02 N. S. Hoang , A. G. Ramm

The Nystr\"om method is a widely used technique for improving the scalability of kernel-based algorithms, including kernel ridge regression, spectral clustering, and Gaussian processes. Despite its popularity, the numerical stability of the…

Numerical Analysis · Mathematics 2025-12-02 Alberto Bucci , Yuji Nakatsukasa , Taejun Park

This work focuses on stability analysis of numerical solutions to jump diffusions and jump diffusions with Markovian switching. Due to the use of Poisson processes, using asymptotic expansions as in the usual approach of treating diffusion…

Optimization and Control · Mathematics 2014-07-11 Zhixin Yang , G. Yin , Haibo Li

The existence, uniqueness, and asymptotic stability of modulo periodic Poisson stable solutions of dynamic equations on a periodic time scale are investigated. The model under investigation involves a term which is constructed via a Poisson…

Dynamical Systems · Mathematics 2022-10-12 Fatma Tokmak Fen , Mehmet Onur Fen

This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal…

Dynamical Systems · Mathematics 2026-03-12 Pragati Dutta , Sachin Bhalekar