Advances in Differential Equations and Control Processes
Volume 17, Issue 3, Pages 231 - 257
(August 2016) http://dx.doi.org/10.17654/DE017030231 |
|
THE EFFECT OF DELAY ON A DIFFUSIVE PREDATOR-PREY SYSTEM WITH HOLLING III FUNCTIONAL RESPONSE AND PREY REFUGE
Haoyu Ren, Xue Cheng and Ruizhi Yang
|
Abstract: In this paper, a delayed diffusive predator-prey system with Holling III functional response and prey refuge subject to Neumann boundary condition is considered. By analyzing characteristic equation, stability of the positive equilibrium and existence of Hopf bifurcation are investigated. Also, explicit formulas for determining the bifurcation direction and the stability of the bifurcating periodic solution are derived by the theory of normal form and center manifold. Some numerical simulations are carried out. |
Keywords and phrases: diffusion, delay, Hopf bifurcation, Holling III functional response, predator-prey. |
|
Number of Downloads: 323 | Number of Views: 1117 |
|