【摘要】 研究和评价了混沌复杂度3种定量分析方法——Lyapunov指数、分维、测度熵,及其它们之间的内在联系,并研究了一种简单有效的测度熵替代方法——近似熵(approx im ate entropy)方法.应用以上方法对Log istic映射复杂度进行了分析.结果表明Lyapunov指数和测度熵的值与复杂度基本呈线性关系,分维数与复杂度的函数关系尚难确定,且与Lyapunov指数、测度熵之间的关系也不明确.更多还原

【Abstract】 Three kinds of chaos’ complexity analysis methods,Lyapunov exponent,fractal and K-S entropy,as well as their relationship,are investigated.Approximate entropy(ApEn) method is also studied.They are applied to analyze the complexity of Logistic map.The conclusion is that Lyapunov exponent and K-S entropy have approximately linear relation with complexity,while it is difficult to determine the relation between fractal and complexity.Furthermore the correlation of fractal and Lyapunov exponent,K-S entropy is not clear now.Finally,ApEn method offers a simple and valid analysis mean to substitute K-S entropy.更多还原