Open Access Open Access  Restricted Access Subscription or Fee Access

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

Nijamuddin Ali

Abstract


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
section.

Keywords


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

Full Text:

PDF

Refbacks

  • There are currently no refbacks.


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information.