https://doi.org/10.1140/epjp/s13360-024-04888-8
Regular Article
Role of fear factor in controlling chaos of a plankton–fish system with prey refuge and an additional food
1
PG Department of Mathematics, Guru Nanak College, 152026, Sri Muktsar Sahib, Punjab, India
2
Department of Applied Sciences and Humanities, Shaheed Bhagat Singh State University, 152004, Ferozepur, Punjab, India
3
Department of Mathematics, JIS College of Engineering, 741235, Kalyani, West Bengal, India
Received:
15
November
2023
Accepted:
8
January
2024
Published online:
31
January
2024
In aquatic ecology, the interactions among phytoplankton, zooplankton and fish populations are a very important aspect to study. Their interdependence on each other can help to stabilize or destabilize the system. This paper analyzes the impact of fear of top predator in a three-species food chain model with phytoplankton refuge and an additional food to top predator. The fear of top predators reduces the growth rate of the middle predator, and the top predator (fish population) is provided with some additional food for lowering the pressure on zooplankton’s to be eaten by the fish population. This paper focuses on investigating the intricate dynamics, sensitivity to parameters and the control of chaotic behavior within the system. The local stability analysis of the feasible equilibrium points is performed. After that, the conditions for the existence of transcritical bifurcation and the Hopf bifurcation are established. The system exhibits chaotic behavior at low levels of fear, transitioning to asymptotic stability as fear levels increase. The introduction of additional food to the fish population and the presence of phytoplankton refuge contribute to the regulation of chaotic dynamics at lower fear levels. All the theoretical results are verified by the help of MATLAB in numerical simulations.
Navneet Rana and Abhijit Sarkar have contributed equally to this work.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
