Dynamics of a Delayed Predator-Prey System with Stage Structure for Predator and Prey (Communications in Mathematical Research, 2021)
In this paper, a predator-prey system with two discrete delays and stagestructure for both the predator and the prey is investigated. The dynamical behaviors such as local stability and local Hopf bifurcation are analyzed by regardingthe possible combinations of the two delays as bifurcating parameter. Some explicitformulae determining the direction of the Hopf bifurcation and the stability of thebifurcating periodic solutions are derived by using the normal form method and thecenter manifold theory. Finally, numerical simulations are presented to support thetheoretical analysis.
Keywords: time delay; stage-structure; Hopf bifurcation; stability; periodic solution.