Periodic regimes in a hybrid dynamical predator-prey system with migration and intraspecific competition

The goal of the paper is to construct and analyze a hybrid model describing patch biocommunity dynamics with variable structure interspecific interactions. Species interaction structure variations are implied by predator’s population migration from a patch caused by food resources lack and patch colonization in a case of its sufficient amount. Methods. The model is presented by a three dimensional nonlinear hybrid system consisting of three dynamical subsystems. Switchings between subsystems are regulated by a patch food attractivity value the notion of which was introduced by one of the authors. Due to a food attractivity usage the system possesses a memory because of which variations of interactions’ structure obtain inertia typical for ecological processes. Results.The following regimes of patch biocommunity are introduced: interspecific interaction, predator’s migration and prey’s dynamics in the absence of predators. Symbolic dynamics corresponding to patch regimes variations is investigated. Results delivering conditions of existence of periodic trajectories in a hybrid system, as well as periodic symbolic regime sequences, are obtained. A bifurcation value of a parameter characterized predator’s resource requirements is determined. Numerical example is given. Conclusion. On the basis of obtained results concerning periodic symbolic regime sequences, expressed via system parameters relations, it is possible to predict a predator population migration from a patch and its recolonization. Moreover, appears a possibility to estimate time periods of recolonization processes which is an important practical problem in ecology.