Hopf Bifurcation Analysis for a Semiratio-Dependent Predator-Prey System with Two Delays. (30th September 2013)

• Record Type: Journal Article
• Authors: Zhao, Ming
• Other Names: Ferrara Massimiliano Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-09-30
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/495072
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : This paper is concerned with a semiratio-dependent predator-prey system with nonmonotonic functional response and two delays. It is shown that the positive equilibrium of the system is locally asymptotically stable when the time delay is small enough. Change of stability of the positive equilibrium will cause bifurcating periodic solutions as the time delay passes through a sequence of critical values. The properties of Hopf bifurcation such as direction and stability are determined by using the normal form method and center manifold theorem. Numerical simulations confirm our theoretical findings.