Stationary distribution and global asymptotic stability of a three-species stochastic food-chain system | Zendy

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Stationary distribution and global asymptotic stability of a three-species stochastic food-chain system

Author(s) -

Hong Qiu,

Wenmin Deng

Publication year - 2017

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1510-52

Subject(s) - mathematics , stationary distribution , simple (philosophy) , stability (learning theory) , distribution (mathematics) , food chain , chain (unit) , exponential stability , statistical physics , mathematical optimization , mathematical analysis , nonlinear system , computer science , markov chain , statistics , ecology , machine learning , quantum mechanics , biology , philosophy , epistemology , physics , astronomy

This paper intends to study some dynamical properties of a stochastic three-dimensional Lotka–Volterra system. Under some mild assumptions, we first introduce a simple method to show that the model has a global and positive solution almost surely. Secondly, we prove that this model has a stationary distribution. Then we study the global asymptotic stability of the positive solution. Finally, some numerical simulations are introduced to illustrate the theoretical results.

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