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Volume 7, Issue 2
Nonlinear Dynamical Behaviour in a Predator-Prey Model with Harvesting

Wei Liu & Yaolin Jiang

DOI: 10.4208/eajam.020916.250217a

East Asian J. Appl. Math., 7 (2017), pp. 376-395.

Published online: 2018-02

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  • Abstract

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.

  • Keywords

Predator-prey system, Holling type IV functional response, periodic solution, bifurcation, Lyapunov function.

  • AMS Subject Headings

92D25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-7-376, author = {Wei Liu and Yaolin Jiang}, title = {Nonlinear Dynamical Behaviour in a Predator-Prey Model with Harvesting}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {7}, number = {2}, pages = {376--395}, abstract = {

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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.020916.250217a}, url = {http://global-sci.org/intro/article_detail/eajam/10755.html} }
TY - JOUR T1 - Nonlinear Dynamical Behaviour in a Predator-Prey Model with Harvesting AU - Wei Liu & Yaolin Jiang JO - East Asian Journal on Applied Mathematics VL - 2 SP - 376 EP - 395 PY - 2018 DA - 2018/02 SN - 7 DO - http://doi.org/10.4208/eajam.020916.250217a UR - https://global-sci.org/intro/article_detail/eajam/10755.html KW - Predator-prey system, Holling type IV functional response, periodic solution, bifurcation, Lyapunov function. AB -

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.

Wei Liu and Yaolin Jiang. (2018). Nonlinear Dynamical Behaviour in a Predator-Prey Model with Harvesting. East Asian Journal on Applied Mathematics. 7 (2). 376-395. doi:10.4208/eajam.020916.250217a
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