Dynamical analysis of a two species amensalism model with Beddington–DeAngelis functional response and Allee effect on the second species

A stochastic prey-predator system in a polluted environment with Beddington-DeAngelis functional response is proposed and analyzed. Firstly, for the system with white noise perturbation, by analyzing the limit system, the existence of boundary periodic solutions and positive periodic solutions is proved and the sufficient conditions for the existence of boundary periodic solutions and positive periodic solutions are derived. And then for the stochastic system, by introducing Markov regime switching, the sufficient conditions for extinction or persistence of such system are obtained. Furthermore, we proved that the system is ergodic and has a stationary distribution when the concentration of toxicant is a positive constant. Finally, two examples with numerical simulations are carried out in order to illustrate the theoretical results.

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Dynamical Analysis of Prey Refuge in a Predator-Prey System with Rosenzweig Functional Response

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.271-273.577 ◽

2011 ◽

Vol 271-273 ◽

pp. 577-580

Author(s):

Zhi Hui Ma ◽

Shu Fan Wang ◽

Wen Ting Wang

Keyword(s):

Functional Response ◽

Stability Property ◽

Dynamical Analysis ◽

Prey Refuge ◽

Predator Prey ◽

Prey System ◽

Stabilizing Effect ◽

The Stability ◽

Prey Refuges

In this paper, we proposed a predator-prey system incorporating Rosenzweig functional response and prey refuges. We will consider the stability property of the equilibria. Our results show that refuges using by prey have stabilizing effect on the considered system.

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Dynamical Analysis of a Stochastic Predator-Prey Model with an Allee Effect

Abstract and Applied Analysis ◽

10.1155/2013/340980 ◽

2013 ◽

Vol 2013 ◽

pp. 1-10 ◽

Cited By ~ 8

Author(s):

Feng Rao

Keyword(s):

Asymptotic Stability ◽

Lyapunov Functions ◽

Allee Effect ◽

Dynamical Analysis ◽

Type Ii ◽

Qualitative Properties ◽

Predator Prey ◽

Predator Prey Model ◽

Stochastic Boundedness ◽

Prey Model

We present and analyze a modified Holling type-II predator-prey model that includes some important factors such as Allee effect, density-dependence, and environmental noise. By constructing suitable Lyapunov functions and applying Itô formula, some qualitative properties are given, such as the existence of global positive solutions, stochastic boundedness, and the global asymptotic stability. A series of numerical simulations to illustrate these mathematical findings are presented.

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Dynamics and pattern formation in a modified Leslie–Gower model with Allee effect and Bazykin functional response

International Journal of Biomathematics ◽

10.1142/s1793524517500735 ◽

2017 ◽

Vol 10 (05) ◽

pp. 1750073 ◽

Cited By ~ 1

Author(s):

Peng Feng

Keyword(s):

Steady State ◽

Pattern Formation ◽

Spatial Pattern ◽

Numerical Simulations ◽

Functional Response ◽

Allee Effect ◽

Turing Instability ◽

Spatial Pattern Formation ◽

The Stability ◽

Steady State Solutions

In this paper, we study the dynamics of a diffusive modified Leslie–Gower model with the multiplicative Allee effect and Bazykin functional response. We give detailed study on the stability of equilibria. Non-existence of non-constant positive steady state solutions are shown to identify the rage of parameters of spatial pattern formation. We also give the conditions of Turing instability and perform a series of numerical simulations and find that the model exhibits complex patterns.

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