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Multistability of extinction states in the toy model for three species

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  • Park, Junpyo

Abstract

Multistability is common feature resulting in nonlinear dynamical systems, and its characteristic can be generally depicted by investigating basin structures of initial conditions for give parameter settings. In this paper, we explore the formation of extinction states according to the change of strength of competition levels in the toy model for three species. Through the linear stability analysis, we find that the extinction state can be stable which is persistent. For specific conditions between intensities of two different competitions, we also found that the extinction state can be either bistable or tristable. In each case, the final state of the system can be characterized sensitively depending on initial conditions. To validate our results, we investigate basin structures of parameters for interspecific competition associated to a strength of intraspecific competition. In addition, we found that coexistence becomes robust as intraspecific competition is intensified relatively to the interspecific competition level. We hope our results can be a chance to suggest the emergence of the multistability according to complex competition structures on systems of many populations.

Suggested Citation

  • Park, Junpyo, 2018. "Multistability of extinction states in the toy model for three species," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 92-98.
    • Handle: RePEc:eee:chsofr:v:114:y:2018:i:c:p:92-98
    DOI: 10.1016/j.chaos.2018.06.021
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    References listed on IDEAS

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    1. Han, Xiaozhuo & Chen, Baoying & Hui, Cang, 2016. "Symmetry breaking in cyclic competition by niche construction," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 66-78.
    2. Park, Junpyo, 2018. "Balancedness among competitions for biodiversity in the cyclic structured three species system," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 425-436.
    3. Mauro Mobilia & Alastair M. Rucklidge & Bartosz Szczesny, 2016. "The Influence of Mobility Rate on Spiral Waves in Spatial Rock-Paper-Scissors Games," Games, MDPI, vol. 7(3), pages 1-12, September.
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    Cited by:

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    2. Park, Junpyo, 2021. "Evolutionary dynamics in the rock-paper-scissors system by changing community paradigm with population flow," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).

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