Deterministic and stochastic dynamics of a modified Leslie-Gower prey-predator system with simplified Holling-type Ⅳ scheme

Lin Li; Wencai Zhao; Lin Li; Wencai Zhao

doi:10.3934/mbe.2021143

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 3: 2813-2831. doi: 10.3934/mbe.2021143

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Deterministic and stochastic dynamics of a modified Leslie-Gower prey-predator system with simplified Holling-type Ⅳ scheme

Lin Li ,
Wencai Zhao ^,

College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Received: 05 January 2021 Accepted: 07 March 2021 Published: 24 March 2021

In this paper, a prey-predator model with modified Leslie-Gower and simplified Holling-type Ⅳ functional responses is proposed to study the dynamic behaviors. For the deterministic system, we analyze the permanence of the system and the stability of the positive equilibrium point. For the stochastic system, we not only prove the existence and uniqueness of global positive solution, but also discuss the persistence in mean and extinction of the populations. In addition, we find that stochastic system has an ergodic stationary distribution under some parameter constraints. Finally, our theoretical results are verified by numerical simulations.
- permanence,
- positive equilibrium point,
- persistence in mean,
- extinction,
- ergodic stationary distribution
Citation: Lin Li, Wencai Zhao. Deterministic and stochastic dynamics of a modified Leslie-Gower prey-predator system with simplified Holling-type Ⅳ scheme[J]. Mathematical Biosciences and Engineering, 2021, 18(3): 2813-2831. doi: 10.3934/mbe.2021143

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Abstract

In this paper, a prey-predator model with modified Leslie-Gower and simplified Holling-type Ⅳ functional responses is proposed to study the dynamic behaviors. For the deterministic system, we analyze the permanence of the system and the stability of the positive equilibrium point. For the stochastic system, we not only prove the existence and uniqueness of global positive solution, but also discuss the persistence in mean and extinction of the populations. In addition, we find that stochastic system has an ergodic stationary distribution under some parameter constraints. Finally, our theoretical results are verified by numerical simulations.

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