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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Consequence of Prey Refuge in a Tri-trophic Prey-dependent Food Chain Model with Intra-specific Competition

Journal of Applied Nonlinear Dynamics 5(2) (2016) 199--219 | DOI:10.5890/JAND.2016.06.007

Nijamuddin Ali$^{1}$; Santabrata Chakravarty$^{2}$

$^{1}$ Department of Education, Katwa College, Dist-Burdwan, West Bengal, India, 713130

$^{2}$ Department of Mathematics, Visva-Bharati, Dist-Birbhum, West Bengal, India, 731235

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Abstract

The present article deals with the influence of a constant proportion of prey refuge in presence of intra-specific competition among predator population of a prey-dependent three species food chain model. The behaviour of the system near the biologically feasible equilibria is thoroughly analyzed. The preliminary results such as boundedness and dissipativeness of the system are established. Stability analysis including local and global stability of the equilibria has been carried out in order to examine the behaviour of the system. The present system experiences Hopf-Andronov bifurcation for suitable choice of the parameter values. The influences of the prey refuge parameters on the dynamical behaviour of the system are exhibited through several plots and discussed at some equilibrium positions. It is worth-noting that prey refuge has stabilization effect in some selected situations and bears the potential to control chaotic dynamics of the system. Hence, prey refuge may be of some use for biological control mechanism. Numerical simulations are performed to validate the applicability of the model under consideration.

Acknowledgments

This research work is supported by Minor Research Project of University Grants Commission, New Delhi, India vide Ref. No. F. No. PSW-021/14-15 (ERO), ID No. WBI-042 dated 03.02.2015.

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