School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China.
School of Preparatory Education, North Minzu University, Yinchuan 750021, China.
Math Biosci Eng. 2021 Jan 22;18(2):1425-1449. doi: 10.3934/mbe.2021074.
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.
在本研究中，我们探讨了一个具有环境噪声的随机时变合作Lotka-Volterra（LV）系统。通过应用 M-矩阵理论，我们证明了该系统整体解的存在唯一性。由于随机时变合作 LV 系统不能显式求解，我们构建了一个 Euler-Maruyama（EM）数值解来逼近系统的精确解。此外，还得到了方案的收敛速度和 p 阶矩有界性。最后，通过数值实验验证了我们的理论结果。
