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September 22, 2026
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Qualitative Analysis of a Modified Leslie-Gower Model with Addictive Allee Effect and Gestation Delay

Discontinuity, Nonlinearity, and Complexity. 2020. Vol. 9. No. 3. P. 461–476.
Seralan V.
Translator: S. R
Editor of translation: S. K

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.

Research target: Mathematics Biology Physics
Language: English
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Keywords: time delayStability analysisHopf bifurcationPrey-predator
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