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A three species dynamical system involving prey–predation, competition and commensalism

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  • Gakkhar, Sunita
  • Gupta, Komal

Abstract

In this paper, a three species dynamical system is explored. The system consisting of two logistically growing competing species and the third species acts as a predator as well as host. It is predating over second species with Holling type II functional response, while first species is benefited from the third species. In addition, the prey species move into a refuge to avoid high predation. The essential mathematical features of the proposed model are studied in terms of boundedness, persistence, local stability and bifurcation. The existence of transcritical bifurcations have been established about two axial points. It has been observed that survival of all three species may be possible due to commensalism. Numerical simulations have been performed to show the Hopf bifurcation about interior equilibrium point. The existence of period-2 solution is observed. Further, the bifurcations of codimension-2 have also been investigated.

Suggested Citation

  • Gakkhar, Sunita & Gupta, Komal, 2016. "A three species dynamical system involving prey–predation, competition and commensalism," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 54-67.
    • Handle: RePEc:eee:apmaco:v:273:y:2016:i:c:p:54-67
    DOI: 10.1016/j.amc.2015.09.036
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    References listed on IDEAS

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    1. Flaaten, Ola, 1991. "Bioeconomics of sustainable harvest of competing species," Journal of Environmental Economics and Management, Elsevier, vol. 20(2), pages 163-180, March.
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    Cited by:

    1. Changhee Yoon & Seungyeon Moon & Heesang Lee, 2022. "Symbiotic Relationships in Business Ecosystem: A Systematic Literature Review," Sustainability, MDPI, vol. 14(4), pages 1-15, February.

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