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In this paper we study a prey–predator dynamical system suitable for species having no overlap between successive generations. Assuming that population evolves in discrete-time steps we investigate the prey refuge effect on prey–predator interactions. Stability analysis is applied in order to investigate the local stability properties of the fixed points of our modified model. Numerical simulation tools, such as parametric basins of attraction, phase plots, bifurcation and Lyapunov exponent diagrams are used in order to study further the complex dynamics of the system. It is shown that our modified prey–predator model exhibits a wider array of dynamics than its continuous counterpart. Adding an average refuge destabilizes the prey–predator interactions via a supercritical Neimark–Sacker bifurcation and several period-doubling bifurcations. Finally, the addition of a large refuge exhibits random-like dynamics leading to outbreaks in the prey population density. We show that reproduction in certain intervals is important and should be taken into account since it could help in the identification of insect pest population outbreaks.

Non-overlapping Generation Species: Complex Prey–Predator Interactions