Dynamical Analysis of a Plateau Pika with Cross-Diffusion under Contraception Control

A plateau pika model with spatial cross-diffusion is investigated. By analyzing the corresponding characteristic equations, the local stability of an coexistence steady state is discussed when d21 is small enough. However, when d21 is large enough, the model shows Turing bifurcation if B2 -4AC > ...

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Main Authors: Xiaoyan Wang, Junyuan Yang, Fengqin Zhang
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2014/402194
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author Xiaoyan Wang
Junyuan Yang
Fengqin Zhang
author_facet Xiaoyan Wang
Junyuan Yang
Fengqin Zhang
author_sort Xiaoyan Wang
collection DOAJ
description A plateau pika model with spatial cross-diffusion is investigated. By analyzing the corresponding characteristic equations, the local stability of an coexistence steady state is discussed when d21 is small enough. However, when d21 is large enough, the model shows Turing bifurcation if B2 -4AC > 0. Furthermore, it is proved that if, R > R0, βK > d and cross-diffusion rates are zero, the positive coexistence steady state is globally asymptotically stable. A nonconstant positive solution bifurcates from the coexistent steady state by the Leray-Schauder degree theory. Numerical simulations are carried out to illustrate the main results.
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spelling doaj-art-177c4d61f604470abbd00a3b65ffaab62025-08-20T02:04:54ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/402194402194Dynamical Analysis of a Plateau Pika with Cross-Diffusion under Contraception ControlXiaoyan Wang0Junyuan Yang1Fengqin Zhang2School of Information and Communication Engineering, North University of China, Shanxi, Taiyuan 030051, ChinaDepartment of Applied Mathematics, Yuncheng University, Shanxi, Yuncheng 044000, ChinaDepartment of Applied Mathematics, Yuncheng University, Shanxi, Yuncheng 044000, ChinaA plateau pika model with spatial cross-diffusion is investigated. By analyzing the corresponding characteristic equations, the local stability of an coexistence steady state is discussed when d21 is small enough. However, when d21 is large enough, the model shows Turing bifurcation if B2 -4AC > 0. Furthermore, it is proved that if, R > R0, βK > d and cross-diffusion rates are zero, the positive coexistence steady state is globally asymptotically stable. A nonconstant positive solution bifurcates from the coexistent steady state by the Leray-Schauder degree theory. Numerical simulations are carried out to illustrate the main results.http://dx.doi.org/10.1155/2014/402194
spellingShingle Xiaoyan Wang
Junyuan Yang
Fengqin Zhang
Dynamical Analysis of a Plateau Pika with Cross-Diffusion under Contraception Control
Discrete Dynamics in Nature and Society
title Dynamical Analysis of a Plateau Pika with Cross-Diffusion under Contraception Control
title_full Dynamical Analysis of a Plateau Pika with Cross-Diffusion under Contraception Control
title_fullStr Dynamical Analysis of a Plateau Pika with Cross-Diffusion under Contraception Control
title_full_unstemmed Dynamical Analysis of a Plateau Pika with Cross-Diffusion under Contraception Control
title_short Dynamical Analysis of a Plateau Pika with Cross-Diffusion under Contraception Control
title_sort dynamical analysis of a plateau pika with cross diffusion under contraception control
url http://dx.doi.org/10.1155/2014/402194
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AT junyuanyang dynamicalanalysisofaplateaupikawithcrossdiffusionundercontraceptioncontrol
AT fengqinzhang dynamicalanalysisofaplateaupikawithcrossdiffusionundercontraceptioncontrol