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Computational capabilities at the edge of chaos for one dimensional systems undergoing continuous transitions
E Estevez-Rams1, D Estevez-Moya2, K Garcia-Medina2
1Facultad de Física, Instituto de Ciencias y Tecnología de Materiales (IMRE), University of Havana, San Lazaro y L, La Habana CP 10400, Cuba.
Abstract:
While there has been a keen interest in studying computation at the edge of chaos for dynamical systems undergoing a phase transition, this has come under question for cellular automata. We show that for continuously deformed cellular automata, there is an enhancement of computation capabilities as the system moves towards cellular automata with chaotic spatiotemporal behavior. The computation capabilities are followed by looking into the Shannon entropy rate and the excess entropy, which allow identifying the balance between unpredictability and complexity. Enhanced computation power shows an increase of excess entropy, while the system entropy density has a sudden jump to values near one. The analysis is extended to a system of non-linear locally coupled oscillators that have been reported to exhibit spatiotemporal diagrams similar to cellular automata.
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