Publication: Research - peer-review › Journal article – Annual report year: 2012
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.
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- Predator-prey model, Cross-diffusion, Turing pattern, Sex structure