Open AccessStability and Hopf bifurcation in a diffusivepredator-prey system incorporating a prey refuge
Author(s) -
Xiaoyuan Chang,
Junjie Wei
Publication year - 2013
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2013.10.979
Subject(s) - center manifold , hopf bifurcation , mathematics , predation , bifurcation , transcritical bifurcation , functional response , saddle node bifurcation , eigenvalues and eigenvectors , stability (learning theory) , mathematical analysis , control theory (sociology) , predator , physics , ecology , computer science , nonlinear system , biology , control (management) , quantum mechanics , machine learning , artificial intelligence
A diffusive predator-prey model with Holling type II functional response and the no-flux boundary condition incorporating a constant prey refuge is considered. Globally asymptotically stability of the positive equilibrium is obtained. Regarding the constant number of prey refuge m as a bifurcation parameter, by analyzing the distribution of the eigenvalues, the existence of Hopf bifurcation is given. Employing the center manifold theory and normal form method, an algorithm for determining the properties of the Hopf bifurcation is derived. Some numerical simulations for illustrating the analysis results are carried out.