The Boundedness of the Partially Truncated Euler-Maruyama Scheme for a Stochastic Age-dependent Cooperative Lotka-Volterra System

ZHANG Mengqing

Acta Mathematicae Applicatae Sinica ›› 2023, Vol. 46 ›› Issue (6) : 865-878.

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PDF(1002 KB)
Acta Mathematicae Applicatae Sinica ›› 2023, Vol. 46 ›› Issue (6) : 865-878.

The Boundedness of the Partially Truncated Euler-Maruyama Scheme for a Stochastic Age-dependent Cooperative Lotka-Volterra System

  • ZHANG Mengqing
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Abstract

In this paper, the random cooperative Lotka-Volterra model with agestructured is selected. Considering the biological background of the model, firstly, we define a truncated function and develop a partially truncated Euler-Maruyama numerical solutions of the model to avoid the explosion phenomenon in the process of numerical discretization. Secondly, the boundedness of the algorithm is proved, and the sufficient conditions for the algorithm to be bounded are obtained. Finally, the numerical simulation of the algorithm is carried out and its results are compared with the EM algorithm. The comparison results are consistent with the theoretical proof in this paper.

Key words

stochastic cooperative Lotka-Volterra model / age-structured / partially truncated Euler-Maruyama method / boundedness

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ZHANG Mengqing. The Boundedness of the Partially Truncated Euler-Maruyama Scheme for a Stochastic Age-dependent Cooperative Lotka-Volterra System. Acta Mathematicae Applicatae Sinica, 2023, 46(6): 865-878

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