Stability and Hopf bifurcation in a diffusivepredator-prey system incorporating a prey refuge

  • Received: 01 February 2013 Accepted: 29 June 2018 Published: 01 June 2013
  • MSC : Primary: 35Q92, 35B32; Secondary: 35B35.

  • A diffusive predator-prey model with Holling type II functionalresponse and the no-flux boundary condition incorporating aconstant prey refuge is considered. Globally asymptoticallystability of the positive equilibrium is obtained. Regarding theconstant number of prey refuge $m$ as a bifurcation parameter, byanalyzing the distribution of the eigenvalues, the existence ofHopf bifurcation is given. Employing the center manifold theoryand normal form method, an algorithm for determining theproperties of the Hopf bifurcation is derived. Some numericalsimulations for illustrating the analysis results are carried out.

    Citation: Xiaoyuan Chang, Junjie Wei. Stability and Hopf bifurcation in a diffusivepredator-prey system incorporating a prey refuge[J]. Mathematical Biosciences and Engineering, 2013, 10(4): 979-996. doi: 10.3934/mbe.2013.10.979

    Related Papers:

  • A diffusive predator-prey model with Holling type II functionalresponse and the no-flux boundary condition incorporating aconstant prey refuge is considered. Globally asymptoticallystability of the positive equilibrium is obtained. Regarding theconstant number of prey refuge $m$ as a bifurcation parameter, byanalyzing the distribution of the eigenvalues, the existence ofHopf bifurcation is given. Employing the center manifold theoryand normal form method, an algorithm for determining theproperties of the Hopf bifurcation is derived. Some numericalsimulations for illustrating the analysis results are carried out.
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    © 2013 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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