| Volume 9, Number 2, 2019, Pages 747-764 DOI：10.11948/2156-907X.20180165 |
| Dynamics of a modified Leslie-Gower model with gestation effect and nonlinear harvesting |
| R. Sivasamy,K. Sathiyanathan,K. Balachandran |
| Keywords:Predator-Prey Model, prey harvesting, Crowley-Martin functional response, stability Analysis, Hopf bifurcation. |
| Abstract: |
| This study focuses on the dynamics of a modified Leslie-Gower predator-prey model where the intake rate of prey is by per capita predator according to Crowley-Martin functional response and prey is harvested through nonlinear harvesting strategy. Further the time-delay $(\tau)$ is imposed to utilize gestation period of predations. We investigate the permanence analysis of proposed system. The local stability of non-delayed model at all possible equilibrium points is studied. It is shown that the given model undergoes Hopf bifurcation around positive equilibrium point with respect to delay parameter $\tau$. Subsequently the stability of Hopf bifurcation and its direction are explored through normal and center manifold theories. The derived theoretical results are justified with the help of numerical simulations. |
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