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Journal of Nonlinear Science

, Volume 29, Issue 1, pp 287–318 | Cite as

Bifurcations in a Diffusive Predator–Prey Model with Beddington–DeAngelis Functional Response and Nonselective Harvesting

  • Xiuli SunEmail author
  • Rong Yuan
  • Luan Wang
Article
  • 148 Downloads

Abstract

In this paper, we discuss the dynamics of a predator–prey model with Beddington–DeAngelis functional response and nonselective harvesting. By using the Lyapunov–Schmidt reduction, we obtain the existence of spatially nonhomogeneous steady-state solution. The stability and existence of Hopf bifurcation at the spatially nonhomogeneous steady-state solution with the change of a specific parameter are investigated by analyzing the distribution of the eigenvalues. We also get an algorithm for determining the bifurcation direction of the Hopf bifurcating periodic solutions near the nonhomogeneous steady-state solution. Finally, we show some numerical simulations to verify our analytical results.

Keywords

Bifurcation Lyapunov–Schmidt reduction Beddington–DeAngelis functional response Nonselective harvesting Reaction–diffusion 

Mathematics Subject Classification

35B32 37K50 35B10 35B35 37G10 37G15 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of MathematicsTaiyuan University of TechnologyTaiyuanChina
  2. 2.School of Mathematical SciencesBeijing Normal UniversityBeijingChina
  3. 3.Faculty of EconomicsShanxi University of Finance and EconomicsTaiyuanChina

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