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Journal of Applied Nonlinear Dynamics 8(4) (2019) 637--653 | DOI:10.5890/JAND.2019.12.009

Sahabuddin Sarwardi, Md. Reduanur Mandal, Nurul Huda Gazi

Department of Mathematics & Statistics, Aliah University, IIA/27, New Town, Kolkata - 700 160, West Bengal, India

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Abstract

In this paper we study a one-consumer-two-resources ecological system with simple mass action and Beddington-DeAngelis functional responses. The essential mathematical features of the present model have been analyzed thoroughly in terms of the local and the global stability and the bifurcations arising in some selected situations as well. The ranges of the significant parameters under which the system admits a Hopf bifurcation are investigated. The explicit formulae for determining the stability, direction and other properties of bifurcating periodic solutions are also derived with the use of both the normal form and the central manifold theory (cf. Carr [1], Hassard et al. [2]). Numerical illustrations are performed finally in order to validate the applicability of the model under consideration.

Acknowledgments

Authors are thankful to the Department of Mathematics, Aliah University for providing opportunities to perform the present work. Dr. Sarwardi is thankful to Mr. Manarul Haque, Ph.D. student, Department of Mathematics, Aliah University for his assistance in plotting the solutions of the present system. Dr. S. Sarwardi is also thankful to his Ph.D. supervisor Prof. Prashanta Kumar Mandal, Department of Mathematics, Visva-Bharati (a Central University) for his continuous encouragement and inspiration.

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