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A new interpretation of chaos

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  • Luo, Chuanwen
  • Wang, Gang
  • Wang, Chuncheng
  • Wei, Junjie

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.

Suggested Citation

  • Luo, Chuanwen & Wang, Gang & Wang, Chuncheng & Wei, Junjie, 2009. "A new interpretation of chaos," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1294-1300.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:3:p:1294-1300
    DOI: 10.1016/j.chaos.2008.05.010
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    References listed on IDEAS

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    1. Sheu, Long-Jye & Chen, Hsien-Keng & Chen, Juhn-Horng & Tam, Lap-Mou & Chen, Wen-Chin & Lin, Kuang-Tai & Kang, Yuan, 2008. "Chaos in the Newton–Leipnik system with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 98-103.
    2. Luo, Chuanwen & Wang, Chuncheng & Wei, Junjie, 2009. "A new characteristic index of chaos," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1831-1838.
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    1. Luo, Chuanwen & Yi, Chundi & Wang, Gang & Li, Longsuo & Wang, Chuncheng, 2009. "The mathematical description of uniformity and related theorems," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2748-2753.

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