Synchronization and desynchronization of self-sustained oscillators by common noise

Goldobin, Denis S.; Pikovsky, Arkady

doi:10.1103/physreve.71.045201

Cited by 166 publications

(179 citation statements)

References 11 publications

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“…There have been a variety of studies regarding this phenomenon [4,5,6,7,8,9,10,11,12]. Among them, Teramae and Tanaka [10] made significant progress in understanding its universality from the viewpoint of nonlinear dynamics.…”

Section: Introductionmentioning

confidence: 99%

Synchrony of limit-cycle oscillators induced by random external impulses

et al. 2005

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The mechanism of phase synchronization between uncoupled limit-cycle oscillators induced by common external impulsive forcing is analyzed. By reducing the dynamics of the oscillator to a random phase map, it is shown that phase synchronization generally occurs when the oscillator is driven by weak external impulses in the limit of large inter-impulse intervals. The case where the inter-impulse intervals are finite is also analyzed perturbatively for small impulse intensity. For weak Poissonian impulses, it is shown that the phase synchronization persists up to the first order approximation.

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Section: Introductionmentioning

confidence: 99%

Synchrony of limit-cycle oscillators induced by random external impulses

et al. 2005

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“…Following previous studies of noise-induced phase synchronization [31,37,10,38,22,20], we introduce a single scalar variable θ i ∈ [0, 2π) that represents the phase of the i-th oscillator. That is, each isolated limit cycle evolves according to the simple phase equationθ i = ω, where ω is the natural frequency of the oscillator and the phase-plane representation of the limit cycle is x * i (t) = x * (θ i (t)).…”

Section: Phase Reduction and Averagingmentioning

confidence: 99%

“…al. [20], based on the theory of noise-induced phase synchronization [31,37,10,29,26,38,22]. The latter is an extension of phase-reduction methods to stochastic limit cycle oscillators that provides an analytical framework for studying the synchronisation of an ensemble of oscillators driven by a common randomly fluctuating input; in the case of the Moran effect such an input would be due to environmental fluctuations.…”

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confidence: 99%

Dispersal and noise: Various modes of synchrony in ecological oscillators

Bressloff

Lai

2012

J. Math. Biol.

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We use the theory of noise-induced phase synchronization to analyze the effects of dispersal on the synchronization of a pair of predator-prey systems within a fluctuating environment (Moran effect). Assuming that each isolated local population acts as a limit cycle oscillator in the deterministic limit, we use phase reduction and averaging methods to derive a Fokker-Planck equation describing the evolution of the probability density for pairwise phase differences between the oscillators. In the case of common environmental noise, the oscillators ultimately synchronize. However the approach to synchrony depends on whether or not dispersal in the absence of noise supports any stable asynchronous states. We also show how the combination of correlated (shared) and uncorrelated (unshared) noise with dispersal can lead to a multistable steady-state probability density.

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“…Reliability increased dramatically at larger noise SDs, until at 97 lV=cm, not only the burst onsets but also the spikes inside bursts were almost perfectly aligned. 9,32,42,55 This extra reliability of spike timing during bursts was quantified by comparing the RR and SR coherences (Fig. 7(b)).…”

Section: Nonlinear Responsesmentioning

confidence: 99%

Sensory coding in oscillatory electroreceptors of paddlefish

Neiman

Russell²

2011

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Coherence and information theoretic analyses were applied to quantitate the response properties and the encoding of time-varying stimuli in paddlefish electroreceptors (ERs), studied in vivo. External electrical stimuli were Gaussian noise waveforms of varied frequency band and strength, including naturalistic waveforms derived from zooplankton prey. Our coherence analyses elucidated the role of internal oscillations and transduction processes in shaping the 0.5-20 Hz best frequency tuning of these electroreceptors, to match the electrical signals emitted by zooplankton prey. Stimulus-response coherence fell off above approximately 20 Hz, apparently due to intrinsic limits of transduction, but was detectable up to 40-50 Hz. Aligned with this upper fall off was a narrow band of intense internal noise at $25 Hz, due to prominent membrane potential oscillations in cells of sensory epithelia, which caused a narrow deadband of external insensitivity. Using coherence analysis, we showed that more than 76% of naturalistic stimuli of weak strength, $1 lV=cm, was linearly encoded into an afferent spike train, which transmitted information at a rate of $30 bits=s. Stimulus transfer to afferent spike timing became essentially nonlinear as the stimulus strength was increased to induce bursting firing. Strong stimuli, as from nearby zooplankton prey, acted to synchronize the bursting responses of afferents, including across populations of electroreceptors, providing a plausible mechanism for reliable information transfer to higher-order neurons through noisy synapses. Rhythmical activity underlies various complex physiological processes in central nervous systems. Peripheral sensory receptors, on the other hand, are often considered as "passive" systems with relatively simple and linear dynamics. Nevertheless, self-sustained oscillations have been observed in several types of peripheral sensory receptors. This paper reports on stimulus encoding in electroreceptors (ERs) of paddlefish, which use passive electrosense to feed on zooplankton. A single peripheral electroreceptor in paddlefish is a complex system comprised of several thousands of sensory epithelial cells innervated by a few primary sensory neurons (afferents). It embeds distinct oscillators: one resides in a population of epithelial cells, synaptically coupled to another oscillator in afferent terminals. In contrast to auditory receptors, which resonate to sound waves of certain frequency, neither epithelial nor afferent rhythms of electroreceptors match the low-frequency bioelectric signals emitted by zooplankton prey. We applied Gaussian noise stimuli to study how oscillators embedded in paddlefish electroreceptors shape the linear and nonlinear responses of electroreceptors, and to characterize quantitatively how external stimuli, including bioelectrical signals from zooplankton prey, are encoded into the timing of afferent firing.

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Synchronization and desynchronization of self-sustained oscillators by common noise

Cited by 166 publications

References 11 publications

Synchrony of limit-cycle oscillators induced by random external impulses

Synchrony of limit-cycle oscillators induced by random external impulses

Dispersal and noise: Various modes of synchrony in ecological oscillators

Sensory coding in oscillatory electroreceptors of paddlefish

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