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 > ...
Saved in:
| Main Authors: | , , |
|---|---|
| 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 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850227209660268544 |
|---|---|
| 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. |
| format | Article |
| id | doaj-art-177c4d61f604470abbd00a3b65ffaab6 |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| 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 |
| work_keys_str_mv | AT xiaoyanwang dynamicalanalysisofaplateaupikawithcrossdiffusionundercontraceptioncontrol AT junyuanyang dynamicalanalysisofaplateaupikawithcrossdiffusionundercontraceptioncontrol AT fengqinzhang dynamicalanalysisofaplateaupikawithcrossdiffusionundercontraceptioncontrol |