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Complexity leads to randomness in chaotic systems

René Lozi


Complexity of a particular coordinated system is the degree of difficulty in predicting the properties of the system if the properties of the system's correlated parts are given. The coordinated system manifests properties not carried by individual parts. The subject system can be said to emerge without any "guiding hand". In systems theory and science, emergence is the way complex systems and patterns arise out of a multiplicity of relatively simple interactions. Emergence is central to the theories of integrative levels and of complex systems. The emergent property of the ultra weak multidimensional coupling of p 1-dimensional dynamical chaotic systems for which complexity leads from chaos to randomness has been recently pointed out. Pseudorandom or chaotic numbers are nowadays used in many areas of contemporary technology such as modern communication systems and engineering applications. Efficient Chaotic Pseudo Random Number Generators (CPRNG) have been recently introduced. They use the ultra weak multidimensional coupling of p 1-dimensional dynamical systems which preserves the chaotic properties of the continuous models in numerical experiments. Together with chaotic sampling and mixing processes, the complexity of ultra weak coupling leads to families of CPRNG which are noteworthy. In this paper we improve again these families using a double threshold chaotic sampling instead of a single one. A window of emergence of randomness for some parameter value is numerically displayed. Moreover we emphasize that a determining property of such improved CPRNG is the high number of parameters used and the high sensitivity to the parameters value which allows choosing it as cipher-keys.
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hal-00627604 , version 1 (29-09-2011)


  • HAL Id : hal-00627604 , version 1


René Lozi. Complexity leads to randomness in chaotic systems. A.H. Siddiqi, R.C. Singh, P. Manchanda. Mathematics in Science and Technology: Mathematical Methods, Models and Algorithms in Science and Technology. Proceedings of the Satellite Conference of ICM, 15-17 August 2010 Delhi, India, World Scientific, pp.93-125, 2011. ⟨hal-00627604⟩
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