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Three Logistic Models for the Two-Species Interactions: Symbiosis, Predator-Prey and Competition

R. Lopez-Ruiz·D. Fournier-Prunaret
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Abstract

If one isolated species is supposed to evolve following the logistic mapping, then we are tempted to think that the dynamics of two species can be expressed by a coupled system of two discrete logistic equations. As three basic relationships between two species are present in Nature, namely symbiosis, predator-prey and competition, three different models are obtained. Each model is a cubic two-dimensional discrete logistic-type equation with its own dynamical properties: stationarity, periodicity, quasi-periodicity and chaos. Furthermore, these models could be considered as the basic ingredients to construct more complex interactions in the ecological networks.

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R. Lopez-Ruiz, D. Fournier-Prunaret. 2004-06-12. Three Logistic Models for the Two-Species Interactions: Symbiosis, Predator-Prey and Competition. https://arxiv.org/abs/nlin/0406020

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