Dynamics of a discrete-time stage-structured predator–prey system with Holling type II response function

Abstract

A discrete-time model of predator–prey dynamics with Holling type II response function is proposed. Each species considered has its age structure which is typical for natural communities. The bifurcations, dynamic modes and a possibility of its shifting are studied for the proposed model. The stability loss of a non-trivial fixed point is realised according to Neimark–Sacker and Feigenbaum scenarios. The phase space structure of multistability areas in which a variation of current numbers of prey or predator can shift the dynamic modes is analysed using basins of attraction. Particular attention is paid to the investigation of the feasible values of the parameters in which the model has a biological meaning. To understand the mechanisms of interspecific interaction influence on each species dynamics in a community, we compare cases with and without interspecific interaction. The presence of interspecific interaction in the community increases the variety of emerging dynamic modes of the predator population size.