Dynamical complexity of a spatial predator–prey model with migration

Spatial component of ecological interactions has been identified as an important factor in how ecological communities are shaped. Thus, in this paper, spatial pattern of a spatial predator–prey model, which is combined with migration and diffusion, is investigated. We present the emergence of spatial pattern by both theoretical analysis and numerical simulations. Our study reveals that migration has great influence on the pattern formation. More specifically, travelling pattern can be induced by it. Furthermore, wavelength of the travelling pattern with respect to the diffusion coefficient of the predator is calculated. The obtained results show that the modeling by both migration and diffusion is useful for studying the dynamic complexity of ecosystems, which well extend the finding of pattern formation in the ecosystems and may well explain the field observed in some areas.