Stability and Bifurcation in a Delayed Holling-Tanner Predator-Prey System with Ratio-Dependent Functional Response. (18th December 2012)

• Record Type: Journal Article
• Authors: Liu, Juan; Zhang, Zizhen; Fu, Ming
• Other Names: Conca C. Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2012(2012)
• Publication Date: 2012-12-18
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2012/384293
• Languages: English
• ISSNs: 1110-757X

Abstract

Abstract : We analyze a delayed Holling-Tanner predator-prey system with ratio-dependent functional response. The local asymptotic stability and the existence of the Hopf bifurcation are investigated. Direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are studied by deriving the equation describing the flow on the center manifold. Finally, numerical simulations are presented for the support of our analytical findings.