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Shape effects on herd behavior in ecological interacting population models

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  • Bulai, Iulia Martina
  • Venturino, Ezio

Abstract

In this paper, we introduce several dynamical systems modeling two-populations interactions. The main idea is to assume that the individuals of one of the populations gather together in herds, thus possess a social behavior, while individuals of the second population show a more individualistic attitude. We model the fact that the interaction between the two populations occurs mainly through the perimeter of the herd in a 2D space or through the total surface area for populations that live in a 3D space. This idea has already been explored earlier, but here we even accommodate the model for herds that assume fractal shapes. We account for all types of the populations intermingling: symbiosis, competition and predator–prey interactions. In the cases of obligated mutualism for the individualistic population and of competition, the stable solution attained by the populations is independent of the shape of the herd.

Suggested Citation

  • Bulai, Iulia Martina & Venturino, Ezio, 2017. "Shape effects on herd behavior in ecological interacting population models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 141(C), pages 40-55.
    • Handle: RePEc:eee:matcom:v:141:y:2017:i:c:p:40-55
    DOI: 10.1016/j.matcom.2017.04.009
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    Citations

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    Cited by:

    1. Kumar, Sachin & Kharbanda, Harsha, 2019. "Chaotic behavior of predator-prey model with group defense and non-linear harvesting in prey," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 19-28.
    2. Gupta, Ashvini & Dubey, Balram, 2022. "Bifurcation and chaos in a delayed eco-epidemic model induced by prey configuration," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    3. Ghanbari, Behzad & Djilali, Salih, 2020. "Mathematical analysis of a fractional-order predator-prey model with prey social behavior and infection developed in predator population," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    4. María Carmen Vera & Marcos Marvá & Víctor José García-Garrido & René Escalante, 2024. "The Beddington–DeAngelis Competitive Response: Intra-Species Interference Enhances Coexistence in Species Competition," Mathematics, MDPI, vol. 12(4), pages 1-23, February.
    5. Castillo-Alvino, Hamlet Humberto & Marvá, Marcos, 2022. "Group defense promotes coexistence in interference competition: The Holling type IV competitive response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 426-445.
    6. Djilali, Salih, 2019. "Impact of prey herd shape on the predator-prey interaction," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 139-148.
    7. Cecilia Berardo & Iulia Martina Bulai & Ezio Venturino, 2021. "Interactions Obtained from Basic Mechanistic Principles: Prey Herds and Predators," Mathematics, MDPI, vol. 9(20), pages 1-18, October.
    8. Jinbu Zhao & Yongyou Nie & Kui Liu & Jizhi Zhou, 2020. "Evolution of the Individual Attitude in the Risk Decision of Waste Incinerator Construction: Cellular Automaton Model," Sustainability, MDPI, vol. 12(1), pages 1-16, January.
    9. Ezio Venturino, 2022. "Disease Spread among Hunted and Retaliating Herding Prey," Mathematics, MDPI, vol. 10(23), pages 1-21, November.
    10. Fu, Shuaiming & Luo, Jianfeng & Zhao, Yi, 2022. "Stability and bifurcations analysis in an ecoepidemic system with prey group defense and two infectious routes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 665-690.
    11. Acotto, Francesca & Venturino, Ezio & Viscardi, Alberto, 2024. "Does a marginal contact with a native species living in a complex domain with a fractional dimension boundary represent a sufficient invasive mechanism for the establishment of a migrating population?," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).

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