Bifurcations in active predator - passive prey model

Bifurcations were studied numerically in the system of partial differential equations, which is a one variant of predator-prey models. The mathematical model takes into account spatial distribution in habitat, active directed predator movements, birth and death process in prey population. The analysis of possible population dynamics development was performed by two qualitatively different discrete sampling techniques (Bubnov-Galerkin’s method and grid method). As a bifurcation parameters the predator quantity and predator reaction rate to spatial non-uniformity of prey population were used. As a result of numerical investigation was found that population under these assumptions can demonstrates a complex bifurcation transitions which leads to various spatio-temporal dynamics: periodic, quasi-periodic and chaotic regimes.