Dynamical Analysis of a Delayed Reaction-Diffusion Predator-Prey System. (30th October 2012)

• Record Type: Journal Article
• Authors: Zhu, Yanuo; Cai, Yongli; Yan, Shuling; Wang, Weiming
• Other Names: Zizovic Malisa R. Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2012(2012)
• Publication Date: 2012-10-30
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2012/323186
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : This work deals with the analysis of a delayed diffusive predator-prey system under Neumann boundary conditions. The dynamics are investigated in terms of the stability of the nonnegative equilibria and the existence of Hopf bifurcation by analyzing the characteristic equations. The direction of Hopf bifurcation and the stability of bifurcating periodic solution are also discussed by employing the normal form theory and the center manifold reduction. Furthermore, we prove that the positive equilibrium is asymptotically stable when the delay is less than a certain critical value and unstable when the delay is greater than the critical value.