Pattern dynamics of a reaction-diffusion predator-prey system with both refuge and harvesting  

作　　者：Lakshmi Narayan Guin Sudipta Pal Santabrata Chakravarty Salih Djilali 

机构地区：[1]Department of Mathematics,Visva-Bharati,Santiniketan 731235,West Bengal,India [2]Department of Mathematics,Universite Hassiba Benbouali de Chlef,Chlef 02000,Algeria Laboratoire d’Analyse Non Linéaire et Mathématiques Appliquées,Universitéde Tlemcen,Tlemcen,Algeria

出　　处：《International Journal of Biomathematics》2021年第1期1-29,共29页生物数学学报（英文版）

基　　金：the financial support in part from Special Assistance Programme(SAP-III)sponsored by the University Grants Commission(UGC),New Delhi,India(Grant No.F.510/3/DRS-III/2015(SAP-I)).Dr.S.Djilali is partially supported by the DGRSDT of Algeria.

摘　　要：We are concerned with a reaction-diffusion predator–prey model under homogeneous Neumann boundary condition incorporating prey refuge(proportion of both the species)and harvesting of prey species in this contribution.Criteria for asymptotic stability(local and global)and bifurcation of the subsequent temporal model system are thoroughly analyzed around the unique positive interior equilibrium point.For partial differential equation(PDE),the conditions of diffusion-driven instability and the Turing bifurcation region in two-parameter space are investigated.The results around the unique interior feasible equilibrium point specify that the effect of refuge and harvesting cooperation is an important part of the control of spatial pattern formation of the species.A series of computer simulations reveal that the typical dynamics of population density variation are the formation of isolated groups within the Turing space,that is,spots,stripe-spot mixtures,labyrinthine,holes,stripe-hole mixtures and stripes replication.Finally,we discuss spatiotemporal dynamics of the system for a number of different momentous parameters via numerical simulations.

关 键 词：Two species reaction-diffusion system ratio-dependent functional response diffusion-driven instability pattern selection stationary patterns 

分 类 号：O17[理学—数学]