CROSS-DIFFUSION INDUCED TURING PATTERNS IN A SEX-STRUCTURED PREDATOR-PREY MODEL

作     者：JIA LIU HUA ZHOU LAI ZHANG 

作者机构：College of Mathematics and Physics Changzhou University Changzhou 213016 P. R. China Department of Mathematics The Technical University of Denmark DK 2800 Lyngby Denmark 

出 版 物：《International Journal of Biomathematics》 (生物数学学报（英文版）)

年 卷 期：2012年第5卷第4期

页      面：39-61页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：NSF of Changzhou University, (JS201002) NSF of Jiangsu Province, (BK2006064) PRC National Natural Science Foundation of China, NSFC, (11071209) 

主　　题：Predator-prey model cross-diffusion turing pattern sex structure. 

摘      要：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.