Open Access Open Access  Restricted Access Subscription or Fee Access

Interactive consequence of prey refuge in a tri-trophic food chain model

Lakshmi Narayan Guin, Satyajit Kundu, Santabrata Chakravarty


The present article appertains to a tri-trophic food chain model of the interacting population, including partial prey refuge and intra-specific competition among the predators. The precursory issues, including boundedness and dissipativeness of the system, are established. The stability analyses corresponding to the feasible equilibria of the present system are carried out systematically with special emphasis on global stability. The system appears to undergo Hopf-bifurcation depending on the appropriate set of model parameter values. In the absence of any intra-specific competition, the system exposes chaotic behaviour which is duly confirmed by Lyapunov exponents. On the contrary, such a chaotic response disappears for a specific value of self-interaction. Attention is also focused on the consequences of prey refuge graphically, which possesses a stabilizing effect and can control the system`s chaotic dynamics, leading to period-doubling and limit cycles. Finally, numerical simulations are performed for the purpose of model validation regarding its applicability in the realm of ecological food chain systems.


Food chain model, Intra-specific competition, Prey refuge, Hopf-bifurcation, Lyapunov function, Chaos, Lyapunov Exponent.

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.