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 Volume 9, Number 2, 2019, Pages 747-764 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. PDF      Download reader