TY - JOUR ID - 9014 TI - Dynamics of a predator-prey system with prey refuge JO - Computational Methods for Differential Equations JA - CMDE LA - en SN - 2345-3982 AU - Lajmiri, Zeynab AU - Orak, Iman AU - Hosseini, Samane AD - Sama technical and vocational training college, Izeh Branch, Islamic Azad University, Izeh, Iran Y1 - 2019 PY - 2019 VL - 7 IS - 3 SP - 454 EP - 474 KW - Hopf Bifurcation KW - Bogdanov-Takens bifurcation KW - Dynamical behavior KW - Limit cycles DO - N2 - 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. UR - https://cmde.tabrizu.ac.ir/article_9014.html L1 - https://cmde.tabrizu.ac.ir/article_9014_f1e76cb4305792b7763e210ead9b349c.pdf ER -