Abstract
The objective of this paper is to study systematically the dynamical properties of a predator-prey model with nonlinear predator harvesting. We show the different types of system behaviors for various parameter values. The results developed in this article reveal far richer dynamics compared to the model without harvesting. The occurrence of change of structure or bifurcation in a system with parameters is a way to predict global dynamics of the system. It has been observed that the model has at most two interior equilibria and can exhibit numerous kinds of bifurcations (e.g. saddle-node, transcritical, Hopf-Andronov and Bogdanov-Takens bifurcation). The stability (direction) of the Hopf-bifurcating periodic solutions has been obtained by computing the first Lyapunov number. The emergence of homoclinic loop has been shown through numerical simulation when the limit cycle arising though Hopf-bifurcation collides with a saddle point. Numerical simulations using MATLAB are carried out as supporting evidences of our analytical findings. The main purpose of the present work is to offer a complete mathematical analysis for the model.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.