Detection and computation of high codimension bifurcations in diffuse predator–prey systems

Abstract

In this paper, we consider reaction–diffusion model with modified Leslie–Gower and Holling-type II functional response and by varying simultaneously three model parameters, our model exhibits different types of complex dynamics. This allowed us to delimit several bifurcation surfaces with higher codimension corresponding to: Turing, Turing-Transcritical, Turing–Bogdanov–Taken, Turing–Hopf–Andronov, Turing-Saddle–node. Moreover by varying at least three bifurcation parameters, we show that small variations in the ratio of the diffusion coefficients can significantly alter bifurcation structure. Finally, the paper ends with the emergence of spatio-temporal patterns via numerical simulations. These simultaneous parameter variations leaded to spatio-temporal local and global bifurcations which are always catastrophic. Our results give new insights about how simultaneous changes in environmental and life history parameters drive different distribution dynamics of predator–prey populations. This only underscores the importance of including global bifurcations in the analysis of food chain models. Such results can be used to improve ecological decision-making on species conservation.