Crucial impact of component Allee effect in predator-prey system (Q6562979)

In this paper, the authors inspect the famous \NHastings and Powell (HP) model [\textit{A. Hastings} and \textit{T. Powell}, Ecology 72, No. 3, 896--903 (1991; \url{doi:10.2307/1940591})]\N incorporating component Allee effect on top predator's reproduction, and analyse the updated model with the help of both analytical and numerical phenomena. Considering cost of Allee effect, half-saturation constant of prey as the key parameters, the Hopf bifurcations are discussed. By using normal form theory introduced in \N[\textit{B. D. Hassard} et al., Theory and applications of Hopf bifurcation. Cambridge etc.: Cambridge University Press (1981; Zbl 0474.34002)], the directions of Hopf bifurcations at the critical values of Allee parameter and half-saturation constant of prey are studied as well. The formulated model indicates that the system demonstrates chaotic, periodic and stable dynamics in the variation of key parameters. The chaos can be controlled for proper application of the large values of parameter used as the cost of Allee effect and also for small values of the parameter used as the half saturation constant of prey population.