Year: 2017
East Asian Journal on Applied Mathematics, Vol. 7 (2017), Iss. 2 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.020916.250217a
East Asian Journal on Applied Mathematics, Vol. 7 (2017), Iss. 2 : pp. 376–395
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Predator-prey system Holling type IV functional response periodic solution bifurcation Lyapunov function.