A phase reduction method for weakly coupled stochastic oscillator systems

Akihisa Ichiki; Yasuomi Sato

doi:10.1007/978-3-642-21105-8_30

A phase reduction method for weakly coupled stochastic oscillator systems

Akihisa Ichiki, Yasuomi Sato

INF - System Information Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We progressively propose a generalized phase reduction method for a stochastic system of weakly coupled oscillators, regardless of the noise intensity, and analyze dynamical behavior in such a system. This is because noise effects on a phase space were so far described for an uncoupled single stochastic oscillator, subjected only to weak noise. Our method is established with definition of "a phase of the distribution of state variables," rather than by defining distributions on a phase space. The stochastic system of weakly coupled oscillators can then be reduced straightforward to one dimensional phase dynamics. It is also confirmed that our method can be applied into the deterministic system without any noise intensity.

Original language	English
Title of host publication	Advances in Neural Networks - 8th International Symposium on Neural Networks, ISNN 2011
Pages	251-259
Number of pages	9
Edition	PART 1
DOIs	https://doi.org/10.1007/978-3-642-21105-8_30
Publication status	Published - 2011 Jun 6
Event	8th International Symposium on Neural Networks, ISNN 2011 - Guilin, China Duration: 2011 May 29 → 2011 Jun 1

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Number	PART 1
Volume	6675 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	8th International Symposium on Neural Networks, ISNN 2011
Country	China
City	Guilin
Period	11/5/29 → 11/6/1

Keywords

a phase reduction method
noise independence
stochastic oscillators
weakly couplings

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-642-21105-8_30

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Cite this

Ichiki, A., & Sato, Y. (2011). A phase reduction method for weakly coupled stochastic oscillator systems. In Advances in Neural Networks - 8th International Symposium on Neural Networks, ISNN 2011 (PART 1 ed., pp. 251-259). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6675 LNCS, No. PART 1). https://doi.org/10.1007/978-3-642-21105-8_30

A phase reduction method for weakly coupled stochastic oscillator systems. / Ichiki, Akihisa; Sato, Yasuomi.

Advances in Neural Networks - 8th International Symposium on Neural Networks, ISNN 2011. PART 1. ed. 2011. p. 251-259 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6675 LNCS, No. PART 1).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Ichiki, A & Sato, Y 2011, A phase reduction method for weakly coupled stochastic oscillator systems. in Advances in Neural Networks - 8th International Symposium on Neural Networks, ISNN 2011. PART 1 edn, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 1, vol. 6675 LNCS, pp. 251-259, 8th International Symposium on Neural Networks, ISNN 2011, Guilin, China, 11/5/29. https://doi.org/10.1007/978-3-642-21105-8_30

Ichiki A, Sato Y. A phase reduction method for weakly coupled stochastic oscillator systems. In Advances in Neural Networks - 8th International Symposium on Neural Networks, ISNN 2011. PART 1 ed. 2011. p. 251-259. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 1). https://doi.org/10.1007/978-3-642-21105-8_30

Ichiki, Akihisa ; Sato, Yasuomi. / A phase reduction method for weakly coupled stochastic oscillator systems. Advances in Neural Networks - 8th International Symposium on Neural Networks, ISNN 2011. PART 1. ed. 2011. pp. 251-259 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 1).

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