Dynamical Behavior of a Stochastic Delayed One-Predator and Two-Mutualistic-Prey Model with Markovian Switching and Different Functional Responses

Dynamical Behavior of a Stochastic Delayed One-Predator and Two-Mutualistic-Prey Model with Markovian Switching and Different Functional Responses

We propose a stochastic delayed one-predator and two-mutualistic-prey model perturbed by white noise and telegraph noise. By the M-matrix analysis and Lyapunov functions, sufficient conditions of stochastic permanence and extinction are established, respectively. These conditions are all dependent o...

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Main Authors: Rensheng He, Zuoliang Xiong, Desheng Hong
Format: Article
Language:English
Published: Hindawi Limited 2016-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2016/8453175
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spelling doaj-b3e5108eb068495bb010133e7078f0852020-11-24T23:21:12ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2016-01-01201610.1155/2016/84531758453175Dynamical Behavior of a Stochastic Delayed One-Predator and Two-Mutualistic-Prey Model with Markovian Switching and Different Functional ResponsesRensheng He0Zuoliang Xiong1Desheng Hong2Department of Mathematics, Nanchang University, Nanchang, Jiangxi 330031, ChinaDepartment of Mathematics, Nanchang University, Nanchang, Jiangxi 330031, ChinaDepartment of Mathematics, Nanchang University, Nanchang, Jiangxi 330031, ChinaWe propose a stochastic delayed one-predator and two-mutualistic-prey model perturbed by white noise and telegraph noise. By the M-matrix analysis and Lyapunov functions, sufficient conditions of stochastic permanence and extinction are established, respectively. These conditions are all dependent on the subsystems’ parameters and the stationary probability distribution of the Markov chain. We also investigate another asymptotic property and finally give two examples and numerical simulations to illustrate main results.http://dx.doi.org/10.1155/2016/8453175
collection DOAJ
language English
format Article
sources DOAJ
author Rensheng He
Zuoliang Xiong
Desheng Hong
spellingShingle Rensheng He
Zuoliang Xiong
Desheng Hong
Dynamical Behavior of a Stochastic Delayed One-Predator and Two-Mutualistic-Prey Model with Markovian Switching and Different Functional Responses
Discrete Dynamics in Nature and Society
author_facet Rensheng He
Zuoliang Xiong
Desheng Hong
author_sort Rensheng He
title Dynamical Behavior of a Stochastic Delayed One-Predator and Two-Mutualistic-Prey Model with Markovian Switching and Different Functional Responses
title_short Dynamical Behavior of a Stochastic Delayed One-Predator and Two-Mutualistic-Prey Model with Markovian Switching and Different Functional Responses
title_full Dynamical Behavior of a Stochastic Delayed One-Predator and Two-Mutualistic-Prey Model with Markovian Switching and Different Functional Responses
title_fullStr Dynamical Behavior of a Stochastic Delayed One-Predator and Two-Mutualistic-Prey Model with Markovian Switching and Different Functional Responses
title_full_unstemmed Dynamical Behavior of a Stochastic Delayed One-Predator and Two-Mutualistic-Prey Model with Markovian Switching and Different Functional Responses
title_sort dynamical behavior of a stochastic delayed one-predator and two-mutualistic-prey model with markovian switching and different functional responses
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2016-01-01
description We propose a stochastic delayed one-predator and two-mutualistic-prey model perturbed by white noise and telegraph noise. By the M-matrix analysis and Lyapunov functions, sufficient conditions of stochastic permanence and extinction are established, respectively. These conditions are all dependent on the subsystems’ parameters and the stationary probability distribution of the Markov chain. We also investigate another asymptotic property and finally give two examples and numerical simulations to illustrate main results.
url http://dx.doi.org/10.1155/2016/8453175
work_keys_str_mv AT renshenghe dynamicalbehaviorofastochasticdelayedonepredatorandtwomutualisticpreymodelwithmarkovianswitchinganddifferentfunctionalresponses
AT zuoliangxiong dynamicalbehaviorofastochasticdelayedonepredatorandtwomutualisticpreymodelwithmarkovianswitchinganddifferentfunctionalresponses
AT deshenghong dynamicalbehaviorofastochasticdelayedonepredatorandtwomutualisticpreymodelwithmarkovianswitchinganddifferentfunctionalresponses
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