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Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 402194, 10 pages
http://dx.doi.org/10.1155/2014/402194
Research Article

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

1School of Information and Communication Engineering, North University of China, Shanxi, Taiyuan 030051, China
2Department of Applied Mathematics, Yuncheng University, Shanxi, Yuncheng 044000, China

Received 6 July 2013; Revised 25 December 2013; Accepted 26 December 2013; Published 18 February 2014

Academic Editor: Seenith Sivasundaram

Copyright © 2014 Xiaoyan Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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 is small enough. However, when is large enough, the model shows Turing bifurcation if . Furthermore, it is proved that if, 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.