Back to Search
Start Over
Turing patterns of a strongly coupled predator–prey system with diffusion effects
- Source :
-
Nonlinear Analysis . Feb2011, Vol. 74 Issue 3, p847-858. 12p. - Publication Year :
- 2011
-
Abstract
- Abstract: The main purpose of this work is to investigate the effects of cross-diffusion in a strongly coupled predator–prey system. By a linear stability analysis we find the conditions which allow a homogeneous steady state (stable for the kinetics) to become unstable through a Turing mechanism. In particular, it is shown that Turing instability of the reaction–diffusion system can disappear due to the presence of the cross-diffusion, which implies that the cross-diffusion induced stability can be regarded as the cross-stability of the corresponding reaction–diffusion system. Furthermore, we consider the existence and non-existence results concerning non-constant positive steady states (patterns) of the system. We demonstrate that cross-diffusion can create non-constant positive steady-state solutions. These results exhibit interesting and very different roles of the cross-diffusion in the formation and the disappearance of the Turing instability. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 0362546X
- Volume :
- 74
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Nonlinear Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 55057021
- Full Text :
- https://doi.org/10.1016/j.na.2010.09.035