A new interpretation of chaos

Chuanwen Luo, Gang Wang, Chuncheng Wang and Junjie Wei

Chaos, Solitons & Fractals, 2009, vol. 41, issue 3, 1294-1300

Abstract: The concepts of uniform index and expectation uniform index are two mathematical descriptions of the uniformity and the mean uniformity of a finite set in a polyhedron. The concepts of instantaneous chaometry (ICM) and k step chaometry (k SCM) are introduced in order to apply the method in statistics for studying the nonlinear difference equations. It is found that k step chaometry is an indirect estimation of the expectation uniform index. The simulation illustrate that the expectation uniform index for the Lorenz System is increasing linearly, but increasing nonlinearly for the Chen’s System with parameter b. In other words, the orbits for each system become more and more uniform with parameter b increasing. Finally, a conjecture is also brought forward, which implies that chaos can be interpreted by its orbit’s mean uniformity described by the expectation uniform index and indirectly estimated by k SCM. The k SCM of the heart rate showes the feeble and old process of the heart.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:41:y:2009:i:3:p:1294-1300

DOI: 10.1016/j.chaos.2008.05.010

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