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

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