ISSN:2325-6192 (print)
ISSN:2325-6206 (online)
Journal of Environmental Accounting and Management
António Mendes Lopes (editor), Jiazhong Zhang(editor)
António Mendes Lopes (editor)

University of Porto, Portugal

Email: aml@fe.up.pt

Jiazhong Zhang (editor)

School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi Province 710049, China

Fax: +86 29 82668723 Email: jzzhang@mail.xjtu.edu.cn

Dynamic Analysis of a Three-Species Food Chain System with Intra-Specific Competition

Journal of Environmental Accounting and Management 9(2) (2021) 127--143 | DOI:10.5890/JEAM.2021.06.003

Lakshmi Narayan Guin$^{1}$, Debdeep Roy$^{1}$, Salih Djilali$^{2,3}$

$^{1}$ Department of Mathematics, Visva-Bharati, Santiniketan-731 235, West Bengal, India

$^{2}$ Department of Mathematics, Universite Hassiba Benbouali de Chlef, Chlef 02000, Algeria

$^3$ Laboratoire d'analyse non-lin'{e}aire et math'{e}matiques appliqu'{e}es. Universit'{e} de Tlemcen, Tlemcen, Alg'{e}rie

Abstract

The present article deals with a state of phase transition from stability to chaos emanated from a three-species food chain model with intra-specific competition. The model takes into account two distinct categories of functional response specifically Holling type II and Beddington-DeAngelis type along with the intra-specific competition among predators as well. The existence of equilibria having ecological feasibility together with stability in their proximity is addressed meticulously for the system. The perception of dissipativeness of the system in the realm of ecological principles is not ruled out however from the present investigation. Following the standard stability analysis, both the local and the global response of the co-existence equilibrium are paid due attention in order to understand the dynamics of the system. The fact that the proposed system experiences Hopf-bifurcation and chaos is note-worthy. Finally, the validity of the analytical results is established through numerical simulation based on model parameter values.

Acknowledgments

The present form of the research manuscript owes much to the constructive suggestions of the referees, whose careful revision we are pleased to acknowledge. We sincerely appreciate for the help from Professor Santabrata Chakravarty, Department of Mathematics, Visva-Bharati while carrying out revision work. The first author gratefully acknowledges the financial support in part from Special Assistance Programme (SAP-III) sponsored by the University Grants Commission (UGC), New Delhi, India (Grant No. F.$510$ / $3$ / DRS-III / $2015$ (SAP-I)). S. Djilali supported partially by DGESTR of Algeria No.C00L03UN130120200004.

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