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Stability and bifurcation of a prey predator model with Qiwu’s growth rate for prey

Nijamuddin Ali


In this article, a prey predator model is considered with Qiwu’s growth rate for prey, Holling type-II response for predation and intra-specific competition among predator populations. The essential mathematical features of the proposed model are analyzed with the help of equilibria, local and global stability analysis, and bifurcation theory. The parametric space under which the system enters into a Hopf-bifurcation has been investigated. Global stability results are obtained by constructing suitable Lyapunov functions. I derive the explicit formula for determining the stability property of bifurcating periodic solutions by using normal form and central manifold theory. Our analytical findings are supported by numerical experiments. Biological implication of the analytical findings are discussed in the conclusion


Prey predator model; Intra-specific competition; Global stability; Hopf-bifurcation; Lyapunov function

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