The 0-1 test algorithm for chaos and its applications

To determine whether a given deterministic nonlinear dynamic system is chaotic or periodic, a novel test approach named zero-one （0-1） test has been proposed recently. In this approach, the regular and chaotic motions can be decided by calculating the parameter K approaching asymptotically to zero or one. In this study, we focus on the 0-1 test algorithm and illustrate the selection of parameters of this algorithm by numerical experiments. To validate the reliability and the universality of this algorithm, it is applied to typical nonlinear dynamic systems, including fractional-order dynamic system.

基于改进0-1测试的多相宏观混合效果混沌表征

针对多相搅拌混合效果的量化特征提取提出一种新思路:利用改进型0-1混沌测试方法表征多相混合过程贝蒂数时间序列的混沌特性,并优化混合效果与评价特征值之间定量协调关系。研究发现,将贝蒂数时间序列的渐进增长率Kc的中值作为混沌检测依据,可更加精确地表征不同混合过程中混沌度的差异性变化。贝蒂数混合效果评价方法表明,零维贝蒂数β0与一维贝蒂数β1之间存在相关性,经验证β0时序的Kc中值和β1时序的Kc中值之间也存在较强的正相关性,理论上更加符合β0和β1的代数拓扑学意义。在此基础上进一步发现基于混沌检测的渐进增长率Kc中值与表征混合效果的贝蒂数指标之间具有相关关系,相关系数为0.645,并且Kc中值表征混合效果的有效性由水动力学实验得到了验证。本研究对于拓展和丰富贝蒂数混合效果评价方法具有重要意义。