Dynamical behavior and control of coupled threshold elements with self-inhibition

H. G. Schuster, M. Le Van Quyen, M. Chavez, J. KÖhler, J. Mayer, J. C. Claussen

Research output: Contribution to journalArticle

Abstract

Coupled threshold elements with self-inhibition display a phase transition to an oscillating state where the elements fire in synchrony with a period T that is of the order of the dead-time caused by self-inhibition. This transition is noise-activated and therefore displays strong collectively enhanced stochastic resonance. For an exponentially decaying distribution of dead-times the transition to the oscillating state occurs, coming from high noise temperatures, via a Hopf bifurcation and coming from low temperatures, via a saddle node bifurcation. The transitions can be triggered externally by noise and oscillating signals. This opens up new possibilities for controlling slow wave sleep.

Original languageEnglish
Pages (from-to)3119-3128
Number of pages10
JournalInternational Journal of Bifurcation and Chaos
Volume19
Issue number9
DOIs
Publication statusPublished - 1 Jan 2009

Fingerprint

Threshold elements
Dynamical Behavior
Hopf bifurcation
Fires
Saddle-node Bifurcation
Synchrony
Stochastic Resonance
Sleep
Phase transitions
Hopf Bifurcation
Temperature
Phase Transition

Keywords

  • Cellular automata
  • Dead-time
  • Excitable systems
  • Self-inhibition
  • Threshold elements

Cite this

Schuster, H. G., Le Van Quyen, M., Chavez, M., KÖhler, J., Mayer, J., & Claussen, J. C. (2009). Dynamical behavior and control of coupled threshold elements with self-inhibition. International Journal of Bifurcation and Chaos, 19(9), 3119-3128. https://doi.org/10.1142/S0218127409024694
Schuster, H. G. ; Le Van Quyen, M. ; Chavez, M. ; KÖhler, J. ; Mayer, J. ; Claussen, J. C. / Dynamical behavior and control of coupled threshold elements with self-inhibition. In: International Journal of Bifurcation and Chaos. 2009 ; Vol. 19, No. 9. pp. 3119-3128.
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Schuster, HG, Le Van Quyen, M, Chavez, M, KÖhler, J, Mayer, J & Claussen, JC 2009, 'Dynamical behavior and control of coupled threshold elements with self-inhibition', International Journal of Bifurcation and Chaos, vol. 19, no. 9, pp. 3119-3128. https://doi.org/10.1142/S0218127409024694

Dynamical behavior and control of coupled threshold elements with self-inhibition. / Schuster, H. G.; Le Van Quyen, M.; Chavez, M.; KÖhler, J.; Mayer, J.; Claussen, J. C.

In: International Journal of Bifurcation and Chaos, Vol. 19, No. 9, 01.01.2009, p. 3119-3128.

Research output: Contribution to journalArticle

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Schuster HG, Le Van Quyen M, Chavez M, KÖhler J, Mayer J, Claussen JC. Dynamical behavior and control of coupled threshold elements with self-inhibition. International Journal of Bifurcation and Chaos. 2009 Jan 1;19(9):3119-3128. https://doi.org/10.1142/S0218127409024694