Qualitative Analysis of a Modified Leslie-Gower Model with Addictive Allee Effect and Gestation Delay
DOI:
https://doi.org/10.5890/DNC.2020.09.008Abstract
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.References
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