Logistic Models for Symbiosis, Predator-Prey, and Competition

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Author(s): Ricardo Lopez-Ruiz (Universidad de Zaragoza, Spain)and Danièle Fournier-Prunaret (Institut National des Sciences Appliquées, France)
Copyright: 2008
Pages: 10
Source title: Encyclopedia of Networked and Virtual Organizations
Source Author(s)/Editor(s): Goran D. Putnik (University of Minho, Portugal)and Maria Manuela Cruz-Cunha (Polytechnic Institute of Cavado and Ave, Portugal)
DOI: 10.4018/978-1-59904-885-7.ch111

Keywords: Information Science Reference / Media & Communications / Social Computing / Virtual Communities & Virtual Reality

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Abstract

If one isolated species (corporation) is supposed to evolve following the logistic mapping, then we are tempted to think that the dynamics of two species (corporations) 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: stationary regime, periodicity, quasi-periodicity, and chaos. We also propose that these models could be useful for thinking in the different interactions happening in the economic world, as for instance for the competition and the collaboration between corporations. Furthermore, these models could be considered as the basic ingredients to construct more complex interactions in the ecological and economic networks.

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