文章基本信息

标题：Lyapunov stability analysis for nonlinear delay systems under random effects and stochastic perturbations with applications in finance and ecology
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作者：Abdulwahab Almutairi ; H. El-Metwally ; M. A. Sohaly 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2021
卷号：2021
期号：1
页码：1
DOI：10.1186/s13662-021-03344-6
出版社：Hindawi Publishing Corporation
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.
关键词：Stochastic delay models ; Stochastic stability ; Mean square stability ; Practical uniform stability ; Exponential stability ; Nicholson’s blowflies model ; Black–Scholes market model