Controlling chaos in three species food chain model with fear effect

Vikas Kumar; Nitu Kumari; Vikas Kumar; Nitu Kumari

doi:10.3934/math.2020056

AIMS Mathematics

2020, Volume 5, Issue 2: 828-842. doi: 10.3934/math.2020056

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Controlling chaos in three species food chain model with fear effect

Vikas Kumar ^,,
Nitu Kumari

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

Received: 30 September 2019 Accepted: 11 December 2019 Published: 31 December 2019
MSC : 34H10, 34K18, 34K20, 37G15

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

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Abstract

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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