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

Mengqing Zhang; Qimin Zhang; Jing Tian; Xining Li; Mengqing Zhang; Qimin Zhang; Jing Tian; Xining Li

doi:10.3934/mbe.2021074

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 2: 1425-1449. doi: 10.3934/mbe.2021074

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Research article

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

1.
School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China
2.
School of Preparatory Education, North Minzu University, Yinchuan 750021, China
3.
Department of Mathematics, Towson University, Towson MD 21252, USA

Received: 10 November 2020 Accepted: 05 January 2021 Published: 22 January 2021

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 $ p $th-moment boundedness of the scheme have also been obtained. Additionally, numerical experiments have been conducted to verify our theoretical results.
- age-dependent cooperative Lotka-Volterra system,
- brownian motion,
- euler-Maruyama numerical solution,
- convergence rate,
- $ p $th-moment,
- error analysis,
- discrete time approximation
Citation: Mengqing Zhang, Qimin Zhang, Jing Tian, Xining Li. The asymptotic stability of numerical analysis for stochastic age-dependent cooperative Lotka-Volterra system[J]. Mathematical Biosciences and Engineering, 2021, 18(2): 1425-1449. doi: 10.3934/mbe.2021074

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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 $ p $th-moment boundedness of the scheme have also been obtained. Additionally, numerical experiments have been conducted to verify our theoretical results.

References

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