Nonlinear Theory and Its Applications, IEICE
Online ISSN : 2185-4106
ISSN-L : 2185-4106
Special Section on Recent Progress in Nonlinear Dynamics in Biological Systems
Improvement effect of measuring phase response curves by using multicycle data
Takashi ImaiToshio Aoyagi
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2016 Volume 7 Issue 2 Pages 58-65

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Abstract

The phase oscillator model can succinctly describe the periodic oscillation observed in many real-world biological systems. In this phase description, the phase response curve (PRC) plays a crucial role in determining the dynamical properties of synchronization. Therefore, it is very important to correctly estimate the PRC in general situations. However, we find that known methods, including the recently proposed WSTA method, often give incorrect PRCs under plausible conditions. To overcome this difficulty, here we propose an improved WSTA method using the multicycle data. As a result, we can obtain the correct PRCs of the oscillatory systems to which the conventional methods are inapplicable. Furthermore, by applying this method to a chaotic system with strong periodicity, we demonstrate that the method provides results effective in predicting the synchronization properties of chaotic systems. These results support the applicability to biological systems frequently exhibiting noisy chaotic behavior with some periodicity.

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© 2016 The Institute of Electronics, Information and Communication Engineers
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