Open Access Open Access  Restricted Access Subscription or Fee Access

Impact of Fear in a Predator-Prey Model with Crowley-Martin Response for Predation

Nijamuddin Ali


Predation process play the key role in the dynamics of predator-prey model. Fear in prey populations on account of predator`s hunting is an important fact in predation process. The aim of this article is to find out the impact of fear among prey populations on the system behavior in a prey dependent predator-prey model of interacting populations. In this model we considered Crowley-Martin response function for predation and intra-specific competition among predator populations. We offer a detailed mathematical analysis of the proposed model to illustrate some of the significant results that has arisen from the interplay of deterministic ecological phenomena and processes. In particular, stability (local and global) and bifurcation (Hopf-Andronov) analysis of this model are conducted for biologically feasible parameters. We attained sufficient conditions to ensure the global stability of the unique positive equilibrium, by using appropriate Lyapunov functions and Lasalle invariance principle. Finally, numerical simulations through computer illustrate the dynamics of the ecological system


Predator-prey model, Fear effect, Intra-specific competition, Stability, Bifurcation, Lyapunov function, Crowley-Martin functional response.

Full Text:


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. Also: DOI is paid service which provided by a third party. We never mentioned that we go for this for our any journal. However, journal have no objection if author go directly for this paid DOI service.