Abstract
In this paper, we present a theoretical analysis of processes of pattern formation that involves organisms distribution and their interaction of spatially distributed population with self as well as cross-diffusion in a Beddington-DeAngelis-type predator-prey model. The instability of the uniform equilibrium of the model is discussed, and the sufficient conditions for the instability with zero-flux boundary conditions are obtained. Furthermore, we present novel numerical evidence of time evolution of patterns controlled by self as well as cross-diffusion in the model, and find that the model dynamics exhibits a cross-diffusion controlled formation growth not only to stripes-spots, but also to hot/cold spots, stripes and wave pattern replication. This may enrich the pattern formation in cross-diffusive predator-prey model.
| Original language | English |
|---|---|
| Pages (from-to) | 2006-2015 |
| Number of pages | 10 |
| Journal | Communications in Nonlinear Science and Numerical Simulation |
| Volume | 16 |
| Issue number | 4 |
| DOIs | |
| State | Published - Apr 2011 |
Keywords
- Beddington-DeAgelis-type functional response
- Cross-diffusion
- Pattern formation
- Predator-prey model