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Riddled basins in complex physical and biological systems

doi: 10.6062/jcis.2009.01.02.0007(Free PDF)

Authors

Ricardo L. Viana, Sabrina Camargo, Rodrigo F. Pereira, Marcos C. Verges, Sergio R. Lopes and Sandro Ely S. Pinto

Abstract

Complex systems have typically more than one attractor, either periodic or chaotic, and their basin structure ultimately determines the final-state predictability. When certain symmetries exist in the phase space, their basins of attraction may be riddled, which means that they are so densely intertwined that it may be virtually impossible to determine the final state, given a finite uncertainty in the determination of the initial conditions. Riddling occurs in a variety of complex systems of physical and biological interest. We review the mathematical conditions for riddling to occur, and present two illustrative examples of this phenomenon: coupled Lorenz-like piecewise-linear maps and a deterministic model for competitive indeterminacy in populations of flour beetles.

Keywords

Riddled basins, basins of attraction, complex systems, chaotic attractors.

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