Abstract—This paper deals with the dynamics of a stage-structured predator-prey system. The immature and mature prey are predated by the predator for which modified Holling type II functional response is considered in the model. The solution of the system is positive and bounded. Stability analysis has been discussed about all possible feasible equilibrium points. The origin and boundary equilibrium points are shown to be globally asymptotically stable. The parameters are identified for which system also admits trans-critical bifurcation about these points. The occurrence of Hopf bifurcation has been shown through numerical simulation about positive interior point. Persistence condition is obtained.

Index Terms—Global stability, Hopf bifurcation, persistence, trans-critical bifurcation.

The authors are with Department of Mathematics, Indian Institute of Technology Roorkee, Uttarakhand, India (email: sungkfma@gmail.com).

Cite: Sunita Gakkhar, Komal Gupta, "Dynamics of a Stage-Structured Predator-Prey Model," International Journal of Applied Physics and Mathematics vol. 7, no. 1, pp. 24-32, 2017.