Journal article
Cross-diffusion induced Turing patterns in a sex-structured predator-prey model
In this paper, we consider a sex-structured predator-prey model with strongly coupled nonlinear reaction diffusion. Using the Lyapunov functional and Leray-Schauder degree theory, the existence and stability of both homogenous and heterogenous steady-states are investigated. Our results demonstrate that the unique homogenous steady-state is locally asymptotically stable for the associated ODE system and PDE system with self-diffusion.
With the presence of the cross-diffusion, the homogeneous equilibrium is destabilized, and a heterogenous steady-state emerges as a consequence. In addition, the conditions guaranteeing the emergence of Turing patterns are derived.
Language: | English |
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Year: | 2012 |
Pages: | 1250016 |
ISSN: | 17937159 and 17935245 |
Types: | Journal article |
DOI: | 10.1142/S179352451100157X |