* Correspondence: [email protected]. cn Department of Mathematics, Southeast University, Nanjing 210096, P. R. China Full list of author information is available at the end of the article Abstract In this article, by using Razumikhin-type technique, we investigate pth moment exponential stability of stochastic functional differential equations with Markovian switching and delayed impulses. Several ...

Abstract This research focuses on the stochastic functional differential equations driven by G-Brownian motion (G-SFDEs) with infinite delay. It is proved that trivial solution of a G-SFDE delay exponentially stable in mean square. An example also presented to illustrate effectiveness obtained theory.

Numerous aspects of the immune system operate on the basis of complex regulatory networks that are amenable to mathematical and computational modeling. Several modeling frameworks have recently been applied to simulating the immune system, including systems of ordinary differential equations, delay differential equations, partial differential equations, agent-based models, and stochastic differ...

This paper is concerned with the almost sure exponential stability of the multidimensional nonlinear stochastic differential delay equation (SDDE) with variable delays of the form dx(t) = f(x(t−δ1(t)), t)dt+g(x(t−δ2(t)), t)dB(t), where δ1, δ2 : R+ → [0, τ ] stand for variable delays. We show that if the corresponding (nondelay) stochastic differential equation (SDE) dy(t) = f(y(t), t)dt + g(y(t...

In this paper we introduce some stability criteria for impulsive fuzzy system of differential equations with finite delay in states. Firstly, a new comparison principle for fuzzy differential system compared to crisp ordinary differential equation, based on a notion of upper quasi-monotone nondecreasing, in N dimentional state space is presented. Furthermore, in order to analyze the stability o...

In this paper, we study a class of impulsive neutral stochastic functional integro-differential equations with infinite delay driven by a standard cylindrical Wiener process and an independent cylindrical fractional Brownian motion (fBm) with Hurst parameter H 2 ð1=2; 1Þ in the Hilbert space. We prove the existence and uniqueness of the mild solution for this kind of equations with the coeffici...

The importance of stochastic differential delay equations (SDDEs) derives from the fact that many of the phenomena witnessed around us do not have an immediate effect from the moment of their occurrence. A patient, for example, shows symptoms of an illness days (or even weeks) after the day in which he or she was infected. In general, we can find many ”systems”, in almost any area of science (m...

Abstract The equivalence of p th ( > 0 ) moment stability between stochastic differential delay equations and their numerical methods is studied under the assumptions that are strongly convergent have bounded in finite time.

We present a family of Python modules for the numerical integration of ordinary, delay, or stochastic differential equations. The key features are that the user enters the derivative symbolically and it is just-intime-compiled, allowing the user to efficiently integrate differential equations from a higher-level interpreted language. The presented modules are particularly suited for large syste...