Hopf bifurcation and Turing instability in the reaction-diffusion Holling-Tanner predator-prey model

• Published in: IMA journal of applied mathematics Vol. 78; no. 2; pp. 287 - 306
• Main Authors: Li, X., Jiang, W., Shi, J.
• Format: Journal Article
• Language: English
• Published: 01.04.2013
• Subjects: Bifurcations; Bistability; Differential equations; Hopf bifurcation; Instability; Mathematical models; Partial differential equations; Stability

The reaction-diffusion Holling-Tanner predator-prey model with Neumann boundary condition is considered. We perform a detailed stability and Hopf bifurcation analysis and derive conditions for determining the direction of bifurcation and the stability of the bifurcating periodic solution. For partia...