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Chaos to Order: Role of Additional Food to Predator in a Food Chain Model

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Abstract

The chaos and its controllability is one of the main objectives of mathematical ecology today. In this paper, we propose a new chaos control technique for a three species predator prey system by supplying additional food to predators. A thorough mathematical analysis in this direction revealed the vital role of quality and quantity of the additional food in the controllability of the predator–prey system. The local stability analysis of boundary and interior equilibrium points of the system are done. We have determined the persistence conditions of the system. Bifurcation analysis of the proposed model is done with respect to quality and quantity of additional food. A Hopf point bifurcation phenomena is introduced to detect periodic behaviour of the system. By varying quality and quantity of additional food one can control the chaotic dynamics of a food chain. We establish that chaotic population dynamics of predator–prey system can be controlled by supplying additional food to predators. This study introduce a new chaos control mechanism in a predator–prey system which has applications in fishery management and biological conservation of prey predator species. This model has a special importance in the systems, such as caves, some small marine islands etc.

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Acknowledgments

The authors are grateful to the editor and reviewers for their valuable comments and suggestions which have immensely improved the content and presentation of this version.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Calcutta, Kolkata, West Bengal, India

    Banshidhar Sahoo & Swarup Poria

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  1. Banshidhar Sahoo
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Correspondence to Banshidhar Sahoo.

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Sahoo, B., Poria, S. Chaos to Order: Role of Additional Food to Predator in a Food Chain Model. Differ Equ Dyn Syst 23, 129–146 (2015). https://doi.org/10.1007/s12591-014-0228-4

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