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

doi:10.1142/S0218127409024694

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

College of Engineering and Physical Sciences

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	3119-3128
Number of pages	10
Journal	International Journal of Bifurcation and Chaos
Volume	19
Issue number	9
DOIs	https://doi.org/10.1142/S0218127409024694
Publication status	Published - 1 Jan 2009

Funding

We thank J. Born, L. Marshall and M. Mölle for very helpful discussions. This work was supported by the Deutsche Forschungsgemeinschaft (DFG) Sonderforschungsbereich SFB 654 “Plastizität und Schlaf” (Plasticity and Sleep).

Keywords

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

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10.1142/S0218127409024694

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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.",

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AU - Mayer, J.

AU - Claussen, J. C.

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AB - 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.

KW - Cellular automata

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KW - Excitable systems

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

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