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Deterministic and stochastic analysis of a two-prey–one-predator system with fear effect and switching behaviour in predation

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Abstract

In this article, we have analysed a two-prey–one-predator system in which predator feeds on the more abundant prey species (switching in predation) and also the reproduction of both prey species is greatly reduced by the presence of predator (fear affect). The goal of this work is to investigate the dynamical characteristics of the system in both deterministic and stochastic environments. Well-posedness of the deterministic system has been justified by analysing the basic dynamical properties of that system. Stability conditions at various feasible equilibrium points are derived in terms of model parameters. The impact of parametric fluctuation has also been investigated on the model dynamics by using local bifurcation analysis. We also have studied the proposed model in a fluctuating environment by considering death rate of each species as stochastic parameter. Our mathematical findings have been justified and illustrated through numerical simulation.

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Acknowledgements

The authors are grateful to the anonymous referees and Professor Jian-Qiao Sun (Editor-in-Chief) for their valuable comments and helpful suggestions, which have helped them to improve the presentation of this work significantly. The research of J.J. Nieto has been partially supported by the Agencia Estatal de Investigacion (AEI) of Spain, cofinanced by the European Fund for Regional Development (FEDER) corresponding to the 2014-2020 multiyear financial framework, project PID2020-113275GB-I00; and by Xunta de Galicia under grant ED431C 2019/02.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, 711103, India

    Amartya Das, Debgopal Sahoo & Guruprasad Samanta

  2. Instituto de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela, 15782, Spain

    Juan J. Nieto

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  1. Amartya Das
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  2. Debgopal Sahoo
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Correspondence to Debgopal Sahoo.

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Das, A., Sahoo, D., Samanta, G. et al. Deterministic and stochastic analysis of a two-prey–one-predator system with fear effect and switching behaviour in predation. Int. J. Dynam. Control 11, 1076–1101 (2023). https://doi.org/10.1007/s40435-022-01028-x

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