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Dynamics of a two-prey one-predator model with fear and group defense: A study in parameter planes

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  • Kumbhakar, Ruma
  • Hossain, Mainul
  • Pal, Nikhil

Abstract

Ecosystems are profoundly affected by the predator–prey relationship. During foraging, prey animals balance food and safety demands, and adopt anti-predator behaviors to increase their survival chances. Many prey animals take steps to reduce their predation risk, including moving to low-risk and less profitable areas, becoming more vigilant, and altering their reproductive strategy. Some prey animals employ the strategy of group defense to reduce their chances of being preyed upon by predators. In the present study, we consider a two-prey one-predator model, where one prey species shows group defense against the predator population while the other does not. We explore the complex dynamics of the system in different parametric planes using isospike and Lyapunov exponent diagrams. We observe several kinds of organized periodic structures, coexistence of different types of attractors, both spike-doubling and spike-bubbling routes to chaos, etc. We also investigate how fear and group defense parameters influence the system’s dynamics and play roles in the survival and extinction of the species.

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  • Kumbhakar, Ruma & Hossain, Mainul & Pal, Nikhil, 2024. "Dynamics of a two-prey one-predator model with fear and group defense: A study in parameter planes," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    • Handle: RePEc:eee:chsofr:v:179:y:2024:i:c:s0960077923013516
    DOI: 10.1016/j.chaos.2023.114449
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    References listed on IDEAS

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    1. Fangyuan Hua & Kathryn E. Sieving & Robert J. Fletcher & Chloe A. Wright, 2014. "Increased perception of predation risk to adults and offspring alters avian reproductive strategy and performance," Behavioral Ecology, International Society for Behavioral Ecology, vol. 25(3), pages 509-519.
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    3. Scott Creel & Paul Schuette & David Christianson, 2014. "Effects of predation risk on group size, vigilance, and foraging behavior in an African ungulate community," Behavioral Ecology, International Society for Behavioral Ecology, vol. 25(4), pages 773-784.
    4. Kumar, Vikas & Kumari, Nitu, 2021. "Bifurcation study and pattern formation analysis of a tritrophic food chain model with group defense and Ivlev-like nonmonotonic functional response," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    5. Evan L Preisser & Daniel I Bolnick, 2008. "The Many Faces of Fear: Comparing the Pathways and Impacts of Nonconsumptive Predator Effects on Prey Populations," PLOS ONE, Public Library of Science, vol. 3(6), pages 1-8, June.
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    7. Kumbhakar, Ruma & Hossain, Mainul & Karmakar, Sarbari & Pal, Nikhil, 2024. "An investigation of the parameter space in a tri-trophic food chain model with refuge," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 37-59.
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