The effect of network topologies on stability and bifurcation in predator-prey patch models

Abstract

This paper investigates how network topologies affect Hopf bifurcations from the perspective of discrete patches. We consider a predator-prey patch model with a Holling type-II predator functional response. Our results demonstrate the stability/instability of the positive equilibrium and reveal the existence of a Hopf bifurcation when the scaling parameter is small. Furthermore, the effect of network topologies on Hopf bifurcation value is considered for a special case.