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Periodic and chaotic events in a discrete model of logistic type for the competitive interaction of two species

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  • López-Ruiz, Ricardo
  • Fournier-Prunaret, Danièle

Abstract

Two symmetrically coupled logistic equations are proposed to mimic the competitive interaction between two species. The phenomena of coexistence, oscillations and chaos are present in this cubic discrete system. This work, together with two other similar ones recently published by the authors, completes a triptych dedicated to the two species relationships present in Nature, namely the symbiosis, the predator–prey and the competition. These models can be used as basic ingredients to build up more complex interactions in the ecological networks.

Suggested Citation

  • López-Ruiz, Ricardo & Fournier-Prunaret, Danièle, 2009. "Periodic and chaotic events in a discrete model of logistic type for the competitive interaction of two species," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 334-347.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:1:p:334-347
    DOI: 10.1016/j.chaos.2008.01.015
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    References listed on IDEAS

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    1. López-Ruiz, Ricardo & Fournier-Prunaret, Danièle, 2005. "Indirect Allee effect, bistability and chaotic oscillations in a predator–prey discrete model of logistic type," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 85-101.
    2. Jef Huisman & Franz J. Weissing, 1999. "Biodiversity of plankton by species oscillations and chaos," Nature, Nature, vol. 402(6760), pages 407-410, November.
    3. Xiang, Zhongyi & Song, Xinyu, 2007. "A model of competition between plasmid-bearing and plasmid-free organisms in a chemostat with periodic input," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1419-1428.
    4. Arcadio Navarro & Ana Rivero, 2001. "High rate of inbreeding in Spanish universities," Nature, Nature, vol. 410(6824), pages 14-14, March.
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