Dynamics of a predator-prey system with prey refuge

Document Type : Research Paper


Sama technical and vocational training college, Izeh Branch, Islamic Azad University, Izeh, Iran


In this paper, we investigate the dynamical complexities of a prey predator model prey refuge providing additional food to predator. We determine dynamical behaviours of the equilibria of this system and characterize codimension 1 and codimension 2 bifurcations of the system analytically. Hopf bifurcation conditions are derived analytically. We especially approximate a family of limit cycles emanating from a Hopf point. The analytical results are in well agreement with the numerical simulation results. Our bifurcation analysis indicates that the system exhibits numerous types of bifurcation  phenomena, including Hopf, and Bogdanov-Takens bifurcations.


Volume 7, Issue 3
July 2019
Pages 454-474
  • Receive Date: 23 February 2018
  • Revise Date: 14 August 2018
  • Accept Date: 20 August 2018
  • First Publish Date: 01 July 2019