TY - JOUR

T1 - Cross-diffusion induced Turing patterns in a sex-structured predator-prey model

A1 - Liu,J.

A1 - Zhou,H.

A1 - Zhang,Lai

AU - Liu,J.

AU - Zhou,H.

AU - Zhang,Lai

PB - World Scientific Publishing Co. Pte. Ltd.

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - Predator-prey model

KW - Cross-diffusion

KW - Turing pattern

KW - Sex structure

U2 - 10.1142/S179352451100157X

DO - 10.1142/S179352451100157X

JO - International Journal of Biomathematics

JF - International Journal of Biomathematics

SN - 1793-5245

IS - 4

VL - 5

ER -