Turing patterns in a predator–prey model on complex networks

Predator–prey model with modified Leslie–Gower and Holling type III schemes governed by reaction–diffusion equations can exhibit diversified pattern formations. Considering that species are usually organized as networks instead of being continuously distributed in space, it is essential to study predator–prey system on complex networks. There are the close relation to discrete predator–prey system and continuous version. Here, we extend predator–prey system from continuous media to random networks via finite volume method. With the help of linear stability analysis, Turing patterns of the Leslie–Gower Holling type III predator–prey model on several different networks are investigated. By contrasting and analyzing numerical simulations, we study the influences of network type, average degree as well as diffusion rate on pattern formations.