Analytical approach to noise effects on synchronization in a system of coupled excitable elements

Keiji Okumura; Masatoshi Shiino

doi:10.1007/978-3-642-17537-4_60

Analytical approach to noise effects on synchronization in a system of coupled excitable elements

Keiji Okumura^*, Masatoshi Shiino

^*Corresponding author for this work

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

2 Citations (Scopus)

Abstract

We report relationships between the effects of noise and applied constant currents on the behavior of a system of excitable elements. The analytical approach based on the nonlinear Fokker-Planck equation of a mean-field model allows us to study the effects of noise without approximations only by dealing with deterministic nonlinear dynamics . We find the similarity, with respect to the occurrence of oscillations involving subcritical Hopf bifurcations, between the systems of an excitable element with applied constant currents and mean-field coupled excitable elements with noise.

Original language	English
Title of host publication	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages	486-493
Number of pages	8
Volume	6443 LNCS
Edition	PART 1
DOIs	https://doi.org/10.1007/978-3-642-17537-4_60
Publication status	Published - 2010
Externally published	Yes
Event	17th International Conference on Neural Information Processing, ICONIP 2010 - Sydney, NSW Duration: 2010 Nov 22 → 2010 Nov 25

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Number	PART 1
Volume	6443 LNCS
ISSN (Print)	03029743
ISSN (Electronic)	16113349

Other

Other	17th International Conference on Neural Information Processing, ICONIP 2010
City	Sydney, NSW
Period	10/11/22 → 10/11/25

Keywords

Bifurcations
Langevin equations
Mean-field model
Noise induced synchronization
Nonequilibrium phase transitions
Nonlinear Fokker-Planck equation
Stochastic limit cycle

ASJC Scopus subject areas

Computer Science(all)
Theoretical Computer Science

Access to Document

10.1007/978-3-642-17537-4_60

Cite this

Okumura, K., & Shiino, M. (2010). Analytical approach to noise effects on synchronization in a system of coupled excitable elements. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (PART 1 ed., Vol. 6443 LNCS, pp. 486-493). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6443 LNCS, No. PART 1). https://doi.org/10.1007/978-3-642-17537-4_60

Analytical approach to noise effects on synchronization in a system of coupled excitable elements. / Okumura, Keiji; Shiino, Masatoshi.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 6443 LNCS PART 1. ed. 2010. p. 486-493 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6443 LNCS, No. PART 1).

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

Okumura, K & Shiino, M 2010, Analytical approach to noise effects on synchronization in a system of coupled excitable elements. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). PART 1 edn, vol. 6443 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 1, vol. 6443 LNCS, pp. 486-493, 17th International Conference on Neural Information Processing, ICONIP 2010, Sydney, NSW, 10/11/22. https://doi.org/10.1007/978-3-642-17537-4_60

Okumura K, Shiino M. Analytical approach to noise effects on synchronization in a system of coupled excitable elements. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). PART 1 ed. Vol. 6443 LNCS. 2010. p. 486-493. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 1). doi: 10.1007/978-3-642-17537-4_60

Okumura, Keiji ; Shiino, Masatoshi. / Analytical approach to noise effects on synchronization in a system of coupled excitable elements. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 6443 LNCS PART 1. ed. 2010. pp. 486-493 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 1).

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abstract = "We report relationships between the effects of noise and applied constant currents on the behavior of a system of excitable elements. The analytical approach based on the nonlinear Fokker-Planck equation of a mean-field model allows us to study the effects of noise without approximations only by dealing with deterministic nonlinear dynamics . We find the similarity, with respect to the occurrence of oscillations involving subcritical Hopf bifurcations, between the systems of an excitable element with applied constant currents and mean-field coupled excitable elements with noise.",

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Analytical approach to noise effects on synchronization in a system of coupled excitable elements

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