Lyapunov stability analysis for nonlinear delay systems under random effects and stochastic perturbations with applications in finance and ecology

Advances in Difference Equations

article

Almutairi, Abdulwahab¹  El-Metwally, H.²  Sohaly, M. A.²  Elbaz, I. M.² 

[1] School of Mathematics, Unaizah College of Sciences and Arts, Qassim University;Mathematics Department, Faculty of Science, Mansoura University;Basic Sciences Department, Faculty of Engineering, The British University in Egypt

关键词: Stochastic delay models;    Stochastic stability;    Mean square stability;    Practical uniform stability;    Exponential stability;    Nicholson’s blowflies model;    Black–Scholes market model;   

DOI  :  10.1186/s13662-021-03344-6

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

This manuscript is involved in the study of stability of the solutions of functional differential equations (FDEs) with random coefficients and/or stochastic terms. We focus on the study of different types of stability of random/stochastic functional systems, specifically, stochastic delay differential equations (SDDEs). Introducing appropriate Lyapunov functionals enables us to investigate the necessary conditions for stochastic stability, asymptotic stochastic stability, asymptotic mean square stability, mean square exponential stability, global exponential mean square stability, and practical uniform exponential stability. Some examples with numerical simulations are presented to strengthen the theoretical results. Using our theoretical study, important aspects of epidemiological and ecological mathematical models can be revealed. In ecology, the dynamics of Nicholson’s blowflies equation is studied. Conditions of stochastic stability and stochastic global exponential stability of the equilibrium point at which the blowflies become extinct are investigated. In finance, the dynamics of the Black–Scholes market model driven by a Brownian motion with random variable coefficients and time delay is also studied.

【 授权许可】

CC BY