Spatiotemporal patterns induced by cross-diffusion in predator prey model with prey herd shape effect  

作　　者：Salih Djilali 

机构地区：[1]Faculty of Exact Sciences and Informatics Mathematics Department,University of Chief Laboratoire D'nalyse Non-Lineaire et Mathematiques Appliquees Universite de Tlemcen,Tlemcen,Algerie

出　　处：《International Journal of Biomathematics》2020年第4期233-270,共38页生物数学学报（英文版）

摘　　要：In this paper,we investigate a predator-prey model with herd behavior and cross-diffusion subject to the zero flux boundary conditions.First,the temporal behavior of the model has been investigated,where Hopf bifurcation has been obtained.Then,by analyzing the characteristic equation it has been proved that the cross-diffusion generate a complex dynamics such as Hopf bifurcation,Turing instability,even Turing-Hopf bifurcation.Further,the impact of the prey herd shape on the spatiotemporal patterns has been discussed.Furthermore,by computing and analyzing the normal form associated with the Turing-Hopf bifurcation point,the spatiotemporal dynamics near the Turing-Hopf bifurcation point has been discussed and allso justified by some numerical simulations.

关 键 词：Mathematical biology BIFURCATION pattern formation asymptotic behavior of solutions 

分 类 号：O17[理学—数学]