Bifurcation involving the contact between the boundaries of different regions. For instance, the contact between the boundary of a chaotic attractor and the boundary of its basin of attraction or the contact between a basin boundary and a critical curve LC are examples of this kind of bifurcation.
Published in Chapter:
Logistic Models for Symbiosis, Predator-Prey, and Competition
Ricardo Lopez-Ruiz (Universidad de Zaragoza, Spain) and Danièle Fournier-Prunaret (Institut National des Sciences Appliquées, France)
Copyright: © 2008
|Pages: 10
DOI: 10.4018/978-1-59904-885-7.ch111
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.