Open AccessSTATIONARY PATTERNS OF A RATIO-DEPENDENT PREDATOR-PREY SYSTEM WITH CROSS-DIFFUSION
Author(s) -
Yuxia Wang,
Wan–Tong Li,
Hongbo Shi
Publication year - 2011
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2011.603164
Subject(s) - diffusion , bounded function , constant (computer programming) , domain (mathematical analysis) , mathematics , boundary (topology) , predation , mathematical analysis , statistical physics , physics , computer science , ecology , thermodynamics , biology , programming language
This paper is concerned with a ratio-dependent predator-prey system with diffusion and cross-diffusion in a bounded domain with no flux boundary condition. We establish the existence and non-existence of non-constant positive steady states (patterns). In particular, we show that under certain hypotheses, the cross-diffusion can create stationary patterns even though the corresponding model without cross-diffusion fails.