Bifurcation study and pattern formation analysis of a tritrophic food chain model with group defense and Ivlev-like nonmonotonic functional response

Kumar, Vikas; Kumari, Nitu

doi:10.1016/j.chaos.2021.110964

Chaos, Solitons & Fractals

2021

DOI: 10.1016/j.chaos.2021.110964

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Bifurcation study and pattern formation analysis of a tritrophic food chain model with group defense and Ivlev-like nonmonotonic functional response

Vikas Kumar

Nitu Kumari

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Cited by 24 publications

References 33 publications

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Trade-off dynamics and chaotic behavior in nonautonomous prey-predator model with group defense

Bhargava,

Dubey

2023

Nonlinear Dyn

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Ecological "trade-off" is prioritising one trait over another. Predators put their lives at danger to pursue dangerous prey, and their injuries can reduce their chances of survival. Prey must "trade-off" between reproduction rate and safety, whereas predators must "trade-off" between food and safety. We present a two-dimensional prey and predator model that takes into account prey logistic growth rate and Monod-Haldane type functional response to reflect prey collective defense. We investigate the cost of fear in order to depict prey trade-off dynamics, and we change the predator's mortality rate by incorporating a function that reflects predator loss as a result of encountering dangerous prey. Our model shows bistability and goes through transcritical bifurcation, saddle node bifurcation, Hopf bifurcation, Bogdanov-Takens bifurcation, Bautin bifurcation, Homoclinic bifurcation, and Limit point of cycle bifurcation.We investigated the effects of our critical parameters on both populations and discovered that predators become extinct if their loss of predator is too high due to encounters with dangerous prey, demonstrating how predators risk their own health for food. We find that fear can lead to global stability in a system by causing the stable and unstable limit cycles to collide. We also see that the degree of seasonality in the level of fearin the nonautonomous model might lead to chaos. Sensitivity analysis, the positivity of the maximal Lyapunov exponent, and the uneven distribution of points observed in the Poincar map shown is an established sign of chaotic nature. We note that variations in intensity of seasonality in carry-over can cause a system to shift under many different periodic windows. The findings presented in this article may be beneficial in comprehending the biological insights derived from investigating prey-predator interactions..

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Trade-off dynamics and chaotic behavior in nonautonomous prey-predator model with group defense

Bhargava,

Dubey

2023

Nonlinear Dyn

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Chaotic response of a Monod–Haldane food-web model system

Guin

Mandal

Pakhira

et al. 2023

Int. J. Dynam. Control

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A Complex Dynamical Study of Spatiotemporal Plankton-Fish Interaction with Effects of Harvesting

Pareek,

Baghel

2023

Iran J Sci

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Bifurcation study and pattern formation analysis of a tritrophic food chain model with group defense and Ivlev-like nonmonotonic functional response

Cited by 24 publications

References 33 publications

Trade-off dynamics and chaotic behavior in nonautonomous prey-predator model with group defense

Trade-off dynamics and chaotic behavior in nonautonomous prey-predator model with group defense

Chaotic response of a Monod–Haldane food-web model system

A Complex Dynamical Study of Spatiotemporal Plankton-Fish Interaction with Effects of Harvesting

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