Dynamical Analysis of a Plateau Pika with Cross-Diffusion under Contraception Control. (18th February 2014)

• Record Type: Journal Article
• Authors: Wang, Xiaoyan; Yang, Junyuan; Zhang, Fengqin
• Other Names: Sivasundaram Seenith Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2014(2014)
• Publication Date: 2014-02-18
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2014/402194
• Languages: English
• ISSNs: 1026-0226

Abstract

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 d 21 is small enough. However, when d 21 is large enough, the model shows Turing bifurcation if B 2 - 4 A C > 0 . Furthermore, it is proved that if, R > R 0, β K > 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.