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Controlling chaos in three species food chain model with fear effect

School of Basic Sciences, Indian Institute of Technology Mandi, Mandi, Himachal Pradesh, 175005, India

Special Issues: 2nd International Conference on Mathematical Modeling, Applied Analysis and Computation (ICMMAAC-19), August 8–10, 2019, JECRC University, Jaipur, India

In this article, we study the impact of fear on the dynamics of a three species food chain model. We propose a model with the assumption that the growth rate of intermediate predator reduces at the cost of fear due to top predator, and the growth rate of prey is suppressed due to the fear of the intermediate predator. We carry out the existence of equilibria, local stability analysis and bifurcation analysis. Our numerical simulation reveals that for a low cost of the fear, system remains chaotic while increase in fear factor leads to stability. Even the large cost of fear causes the population to become extinct. We conclude that the fear effect can stabilize the chaotic dynamics of the system.
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Keywords fear effect; local stability; bifurcation; chaos; numerical simulation

Citation: Vikas Kumar, Nitu Kumari. Controlling chaos in three species food chain model with fear effect. AIMS Mathematics, 2020, 5(2): 828-842. doi: 10.3934/math.2020056

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