Dynamics in a predator–prey model with space and noise

摘要

In this paper, we presented a predator–prey model with spatial diffusion and density-dependent noise. It was found that the spatial model without noise has spotted pattern. However, combined with density-dependent noise, the predator–prey model exhibits transition from spotted to labyrinth pattern. Furthermore, when noise intensity and temporal correlation are in appropriate levels, the populations will extinct. The obtained results suggest that stochastic factors may play an important role in populations dynamics, which well enrich the findings in predator–prey models.