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Analysis Method of Period Sensitivities for Rhythm Phenomena

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.