Analysis Method of Period Sensitivities for Rhythm Phenomena
Analysis Method of Period Sensitivities for Rhythm Phenomena
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DOI：
10.1109/smc53654.2022.9945164
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发表时间：
2022-10
期刊：
影响因子：
--
通讯作者：
Y. Kuroe;Y. Mori
中科院分区：
文献类型：
--
作者：
Y. Kuroe;Y. Mori
在任何系统的分析和设计中，灵敏度分析都是基础和必要的。本文讨论了一种对存在于物理系统、生物系统和人类社会等各种系统中的节奏现象进行灵敏度分析的方法。由于在非线性系统中，节奏作为周期现象是自主出现的，因此对节奏现象的敏感性分析是一个非常困难的问题。对周期现象进行了讨论，提出了一种周期敏感性分析方法。首先通过引入庞卡罗图，推导出周期敏感性的严格表达式。在此基础上，推导出周期灵敏度计算的有效算法。结果表明，所提出的分析方法不仅可以得到嵌入混沌吸引子中的稳定周期轨道的周期灵敏度，也可以得到嵌入混沌吸引子中的不稳定周期轨道的周期灵敏度。
Sensitivity analysis is fundamental and essential in analysis and design in any system. This paper discusses a method of sensitivity analysis of rhythm phenomena which are found in various systems such as physical systems, biological systems and human societies and so on. Sensitivity analysis of rhythm phenomena is very difficult because rhythms appear autonomously as periodic phenomena in nonlinear systems and only few studies have been done. We deal with the periods and propose an analysis method of sensitivities of periods for periodic phenomena. We first derive a strict expression of period sensitivities by introducing Poincaré map. Based on the expression we derive an efficient computer algorithm to calculate period sensitivities. It is shown that the proposed analysis method makes it possible to obtain period sensitivities of not only stable periodic orbits but also unstable periodic orbits embedded in chaos attracters.