Open Access Open Access  Restricted Access Subscription or Fee Access

Effect of prey refuge in a tri-trophic food chain model with Monod-Haldane type response function

Lakshmi Narayan Guin, Sk Mosaraf Ahammed, Muniyagounder Sambath


The present paper deals with the control of a constant proportion of prey refuge in the presence of intra-specific competition among adult predator species of a continuous time food chain model. Dynamic behaviour of the model close to the biologically meaningful feasible equilibria is examined in detail. The preliminary results such as positivity and boundedness of the proposed system are well-recognized. Stability analysis together with the local and global stability of the equilibria has been carried out in order to scrutinize the behaviour of the system. The Hopf-bifurcation analysis of the model with respect to the significant parameter has been explored both analytically and numerically. The effects of the prey refuge parameters on the dynamical behaviour of the system are displayed through a number of valid figures. Also, effects of intra-specific competition among adult predators on the system are exposed by different diagrams. Such outcomes can be exercised to recover ecological decision-making on species protection.


Nonlinear dynamics, Mathematical biology, Dynamical systems in biology, Numerical simulation.

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.