Existence of spatiotemporal patterns in the reaction-diffusion predator-prey model incorporating prey refuge  

作　　者：Lakshmi Narayan Guin Benukar Mondal Santabrata Chakravarty 

机构地区：[1]Department of Mathematics, Visva-BharatiSantiniketan-731 235, West Bengal, India

出　　处：《International Journal of Biomathematics》2016年第6期87-111,共25页生物数学学报（英文版）

摘　　要：The pattern formation in reaction-diffusion system has long been the subject of interest to the researchers in the domain of mathematical ecology because of its universal exis- tence and importance. The present investigation deals with a spatial dynamics of the Beddington-DeAngelis predator-prey model in the presence of a constant proportion of prey refuge. The model system representing boundary value problem under study is subjected to homogeneous Neumann boundary conditions. The asymptotic stability including the local and the global stability and the bifurcation as well of the unique pos- itive homogeneous steady state of the corresponding temporal model has been analyzed. The Turing instability region in two-parameter space and the condition of diffusion- driven instability of the spatiotemporal model are investigated. Based on the appro- priate numerical simulations, the present model dynamics in Turing space appears to get influenced by prey refuge while it exhibits diffusion-controlled pattern formation growth to spots, stripe-spot mixtures, labyrinthine, stripe-hole mixtures and holes repli- cation. The results obtained appear to enrich the findings of the model system under consideration.

关 键 词：Beddington DeAngelis functional response prey refuge STABILITY reaction-diffusion predator-prey model spatiotemporal pattern. 

分 类 号：O175.2[理学—数学] Q141[理学—基础数学]