The asymptotic stability of numerical analysis for stochastic age-dependent cooperative Lotka-Volterra system

Abstract

In this study, we explore a stochastic age-dependent cooperative Lotka-Volterra (LV) system with an environmental noise. By applying the theory of M-matrix, we prove the existence and uniqueness of the global solution for the system. Since the stochastic age-dependent cooperative LV system cannot be solved explicitly, we then construct an Euler-Maruyama (EM) numerical solution to approach the exact solution of the system. The convergence rate and the pth-moment boundedness of the scheme have also been obtained. Additionally, numerical experiments have been conducted to verify our theoretical results.

Keywords

• age-dependent cooperative lotka-volterra system
• brownian motion
• euler-maruyama numerical solution
• convergence rate
• pth-moment
• error analysis
• discrete time approximation