Chaos emergence and dissipation in a three-species food web model with intraguild predation and cooperative hunting

Nazmul Sk; Bapin Mondal; Abhijit Sarkar; Shyam Sundar Santra; Dumitru Baleanu; Mohamed Altanji; Nazmul Sk; Bapin Mondal; Abhijit Sarkar; Shyam Sundar Santra; Dumitru Baleanu; Mohamed Altanji

doi:10.3934/math.2024051

AIMS Mathematics

2024, Volume 9, Issue 1: 1023-1045. doi: 10.3934/math.2024051

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Research article

Chaos emergence and dissipation in a three-species food web model with intraguild predation and cooperative hunting

1.
Department of Mathematics, University of Kalyani, Kalyani 741235, India
2.
Department of Applied Mathematics, University of Calcutta, Kolkata 700009, India
3.
Department of Mathematics, JIS College of Engineering, Kalyani 741235, India
4.
Department of Computer Science and Mathematics, Lebanese American University, Beirut 11022801, Lebanon
5.
Institute of Space Sciences, Magurele-Bucharest, Magurele 077125, Romania
6.
Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia

Received: 17 August 2023 Revised: 17 October 2023 Accepted: 19 October 2023 Published: 05 December 2023
MSC : 34D35, 37C75, 37G15, 92B05

We explore the dynamics of a three-species Lotka-Volterra model incorporating intraguild (IG) predation. The model encompasses interactions between a basal prey, intraguild prey and omnivorous top/intraguild predator. These interactions are characterized by linear functional responses, while considering intraspecific competition and cooperative hunting dynamics. The study involves a comprehensive stability of different steady states and bifurcation analysis. Bifurcation structures unveil shifts in equilibrium stability and the emergence of new equilibrium states. Investigation into dynamics around the coexistence equilibrium highlights diverse behaviors, including stable coexistence, oscillations and chaos. Furthermore, exploration of species' densities under parameter variations uncovers distinct patterns, ranging from stability to chaos. Incorporating the concept of hunting cooperation among IG predators and IG prey can lead to the emergence or suppression of chaotic oscillations, respectively. Additionally, we observe that lower consumption rate of IG predator and cooperation of IG predator helps the system to keep in a stable state position.
- food web,
- intraguild predation,
- hunting cooperation,
- chaos,
- stability,
- bifurcations
Citation: Nazmul Sk, Bapin Mondal, Abhijit Sarkar, Shyam Sundar Santra, Dumitru Baleanu, Mohamed Altanji. Chaos emergence and dissipation in a three-species food web model with intraguild predation and cooperative hunting[J]. AIMS Mathematics, 2024, 9(1): 1023-1045. doi: 10.3934/math.2024051

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Abstract

We explore the dynamics of a three-species Lotka-Volterra model incorporating intraguild (IG) predation. The model encompasses interactions between a basal prey, intraguild prey and omnivorous top/intraguild predator. These interactions are characterized by linear functional responses, while considering intraspecific competition and cooperative hunting dynamics. The study involves a comprehensive stability of different steady states and bifurcation analysis. Bifurcation structures unveil shifts in equilibrium stability and the emergence of new equilibrium states. Investigation into dynamics around the coexistence equilibrium highlights diverse behaviors, including stable coexistence, oscillations and chaos. Furthermore, exploration of species' densities under parameter variations uncovers distinct patterns, ranging from stability to chaos. Incorporating the concept of hunting cooperation among IG predators and IG prey can lead to the emergence or suppression of chaotic oscillations, respectively. Additionally, we observe that lower consumption rate of IG predator and cooperation of IG predator helps the system to keep in a stable state position.

References

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