Spiral Pattern Formation in a Hassell-Varley Predator-Prey Model#

This paper reports an investigation of the emergence of a ratio-dependent predator-prey system with Hassell-Varley-type functional response and reaction diffusion. The instability of the uniform equilibrium of the model is discussed. The conditions for Hopf and Turing bifurcation are obtained in a spatial domain. Furthermore, spatial pattern formation is illustrated by means of numerical simulation, which shows that different parameters lead to different patterns. The result can be expected to have far-reaching influence on real bionomics and may help us to understand better the dynamics of ecosystems.