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Discontinuity, Nonlinearity, and Complexity 9(3) (2020) 461--476 | DOI:10.5890/DNC.2020.09.008

S. Vinoth$^{1}$, R. Sivasamy$^{1}$,$^{2}$, K. Sathiyanathan$^{1}$

$^{1}$ Department of Mathematics, SRMV College of Arts and Science, Coimbatore, Tamil Nadu, India

$^{2}$ Department of Science and Humanities, M.Kumarasamy College of Engineering, Tamil Nadu, India

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Abstract

This paper explores on the qualitative analysis of a modified Leslie-Gower prey-predator model where the consumption rate of prey is according to Beddington-DeAngelis functional response and Allee effect on prey population. Moreover time-lag (τ) is established to exploit gestation period of predations. The permanence analysis of proposed system is investigated. Then we study the local stability of non-delayedmodel at all possible equilibriumpoints and it is demonstrated that the given model experiences Hopf bifurcation about interior equilibrium point with respect to delay τ . Thereafter the stability and direction of Hopf bifurcation are formulated through normal and centermanifold theorems. The derived criteria are justified with the help of numerical simulations.

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