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Nonlinear Dynamical Behaviour in a Predator-Prey Model with Harvesting

  • Wei Liu (a1) (a2) and Yaolin Jiang (a1)

We investigate the stability and periodic orbits of a predator-prey model with harvesting. The model has a biologically-meaningful interior, an attractor undergoing damped oscillations, and can become destabilised to produce periodic orbits via a Hopf bifurcation. Some sufficient conditions for the existence of the Hopf bifurcation are established, and a stability analysis for the periodic solutions using a Lyapunov function is presented. Finally, some computer simulations illustrate our theoretical results.

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*Corresponding author. Email addresses: (W. Liu), (Y.L. Jiang)
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[1] L.S. Chen , Mathematical Models and Methods in Ecology (in Chinese), Science Press, Beijing (1988).

[2] P. Yodzis , Predator-prey theory and management of multispecies fisheries, Ecol. Appl. 4, 5158 (1994).

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[12] T.K. Kar and U.K. Pahari , Non-selective harvesting in prey-predator models with delay, Commun. Nonlinear Sci. Numer. Simul. 11, 499509 (2006).

[15] B.S. Chen and J.J. Chen , Complex dynamic behaviors of a discrete predator-prey model with stage-structure and harvesting, Int. J. Biomath. 10, 1750013 (2017).

[17] J. Guckenheimer and P. Holmes , Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer, New York (1983).

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East Asian Journal on Applied Mathematics
  • ISSN: 2079-7362
  • EISSN: 2079-7370
  • URL: /core/journals/east-asian-journal-on-applied-mathematics
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