Coherence resonance and polymodality in inhibitory coupled excitable oscillators

Volkov, E.I.; Stolyarov, Maksim N.; Zaikin, Alexey; Kurths, Jürgen

doi:10.1103/physreve.67.066202

Cited by 18 publications

(8 citation statements)

References 32 publications

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“…A similar effect has been reported in coupled excitable elements [37,38]. Here, in contrast, we show that the phenomenon can arise in single excitable elements.…”

Section: Discussionmentioning

confidence: 38%

Optimizing periodicity and polymodality in noise-induced genetic oscillators

2011

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Many cellular functions are based on the rhythmic organization of biological processes into self-repeating cascades of events. Some of these periodic processes, such as the cell cycles of several species, exhibit conspicuous irregularities in the form of period skippings, which lead to polymodal distributions of cycle lengths. A recently proposed mechanism that accounts for this quantized behavior is the stabilization of a Hopf-unstable state by molecular noise. Here we investigate the effect of varying noise in a model system, namely an excitable activator-repressor genetic circuit, that displays this noise-induced stabilization effect. Our results show that an optimal noise level enhances the regularity (coherence) of the cycles, in a form of coherence resonance. Similar noise levels also optimize the multimodal nature of the cycle lengths. Together, these results illustrate how molecular noise within a minimal gene regulatory motif confers robust generation of polymodal patterns of periodicity.

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“…A similar effect has been reported in coupled excitable elements [37,38]. Here, in contrast, we show that the phenomenon can arise in single excitable elements.…”

Section: Discussionmentioning

confidence: 38%

Optimizing periodicity and polymodality in noise-induced genetic oscillators

2011

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mentioning

confidence: 78%

“…Coherence resonance has been confirmed in several experimental situations, such as in laser systems [6]. Furthermore, it has also been predicted in a system with two chaotic attractors [7] and in excitable media coupled via an inhibitor concentration, provided the coupled elements behave in antiphase [8].A complete understanding of these different mechanisms of coherence resonance is very important for the study of rhythm generation in biological systems [2,9] and, in particular, in neural tissue. On the other hand, increasing experimental evidence has established in recent years that certain types of neurons frequently operate in a bistable regime [10].…”

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confidence: 89%

Doubly Stochastic Coherence via Noise-Induced Symmetry in Bistable Neural Models

et al. 2003

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The generation of coherent dynamics due to noise in an activator-inhibitor system describing bistable neural dynamics is investigated. We show that coherence can be induced in deterministically asymmetric regimes via symmetry restoration by multiplicative noise, together with the action of additive noise which induces jumps between the two stable steady states. The phenomenon is thus doubly stochastic, because both noise sources are necessary. This effect can be understood analytically in the frame of a small-noise expansion and is confirmed experimentally in a nonlinear electronic circuit. Finally, we show that spatial coupling enhances this coherent behavior in a form of system-size coherence resonance.

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“…Noise amplitude variation results in changes in the extent of coherence in the system's behavior, because the attractors with different time scales are induced by different noise intensities. The possibility of manipulating the extent of coherence in this way has already been demonstrated experimentally 44 and numerically 45 for systems of two and three coupled excitable elements.…”

Section: Review Of the Dynamics Evoked By Inhibitory Couplingmentioning

confidence: 97%

Stochastic multiresonance in the coupled relaxation oscillators

Volkov

Ullner

Kurths

2005

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We study the noise-dependent dynamics in a chain of four very stiff excitable oscillators of the FitzHugh-Nagumo type locally coupled by inhibitor diffusion. We could demonstrate frequency- and noise-selective signal acceptance which is based on several noise-supported stochastic attractors that arise owing to slow variable diffusion between identical excitable elements. The attractors have different average periods distinct from that of an isolated oscillator and various phase relations between the elements. We explain the correspondence between the noise-supported stochastic attractors and the observed resonance peaks in the curves for the linear response versus signal frequency.

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Coherence resonance and polymodality in inhibitory coupled excitable oscillators

Cited by 18 publications

References 32 publications

Optimizing periodicity and polymodality in noise-induced genetic oscillators

Optimizing periodicity and polymodality in noise-induced genetic oscillators

Doubly Stochastic Coherence via Noise-Induced Symmetry in Bistable Neural Models

Stochastic multiresonance in the coupled relaxation oscillators

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