Transition to Diffusion Chaos in a Model of a “Predator–Prey” System with a Lower Threshold for the Prey Population

We carry out an analytical and numerical analysis of a model of the “predator–prey” system with a lower prey population threshold. The model is described by a system of partial differential equations of the “reaction–diffusion” type. Conditions are found for the bifurcation of periodic spatially homogeneous and spatially inhomogeneous solutions from the system thermodynamic branch. It is shown that transition to diffusion chaos in the model occurs in full agreement with the universal Feigenbaum–Sharkovskii–Magnitskii bifurcation theory via a subharmonic cascade of bifurcations of stable limit cycles.