Robustness of the Noise-Induced Phase Synchronization in a General Class of Limit Cycle Oscillators

Teramae, Jun-nosuke; Tanaka, Dan

doi:10.1103/physrevlett.93.204103

Cited by 324 publications

(344 citation statements)

References 30 publications

Supporting

Mentioning

324

Contrasting

Order By: Relevance

“…The first observation is entirely expected, as the situation is identical to that of single phase oscillators, for which it is well known that λ max < 0 [51,46,26,31]. Observation (2) suggests a competition between the entraining effects of the stimulus and the destabilizing effects of the coupling: increasing stimulus amplitude (with other parameters fixed) leads to greater reliability, while increasing coupling strength leads to less reliable responses.…”

Section: For Fixed a λ Max Decreases With ε (Provided ε Is Not Too Smentioning

confidence: 75%

“…Single Theta neurons in isolation will not produce raster plots like that in Fig. 2(b), for they are always reliable [46,51].…”

Section: Neuronal Reliability and Lyapunov Exponentsmentioning

confidence: 99%

“…Theoretical studies have found that models of isolated neurons tend to be reliable [57,46,51,40,22]; here, we undertake a corresponding study for large networks. Two of the known reasons that networks might display unreliability are noise and dynamical instability.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Spike-time reliability of layered neural oscillator networks

Lin¹,

Shea‐Brown²,

Young³

2013

AIP Conference Proceedings

View full text Add to dashboard Cite

We study the reliability of layered networks of coupled "type I" neural oscillators in response to fluctuating input signals. Reliability means that a signal elicits essentially identical responses upon repeated presentations, regardless of the network's initial condition. We study reliability on two distinct scales: neuronal reliability, which concerns the repeatability of spike times of individual neurons embedded within a network, and pooled-response reliability, which concerns the repeatability of total synaptic outputs from a subpopulation of the neurons in a network. We find that neuronal reliability depends strongly both on the overall architecture of a network, such as whether it is arranged into one or two layers, and on the strengths of the synaptic connections. Specifically, for the type of single-neuron dynamics and coupling considered, single-layer networks are found to be very reliable, while two-layer networks lose their reliability with the introduction of even a small amount of feedback. As expected, pooled responses for large enough populations become more reliable, even when individual neurons are not. We also study the effects of noise on reliability, and find that noise that affects all neurons similarly has much greater impact on reliability than noise that affects each neuron differently. Qualitative explanations are proposed for the phenomena observed.

show abstract

Section: For Fixed a λ Max Decreases With ε (Provided ε Is Not Too Smentioning

confidence: 75%

“…Single Theta neurons in isolation will not produce raster plots like that in Fig. 2(b), for they are always reliable [46,51].…”

Section: Neuronal Reliability and Lyapunov Exponentsmentioning

confidence: 99%

See 1 more Smart Citation

Spike-time reliability of layered neural oscillator networks

Lin¹,

Shea‐Brown²,

Young³

2013

AIP Conference Proceedings

View full text Add to dashboard Cite

show abstract

“…Performing the phase reduction for this system as in Sect. 3.1 yields the dimensional phase equation (Teramae et al 2009;Teramae and Tanaka 2004)…”

Section: Robustness To Weak Somatic Noisementioning

confidence: 99%

The robustness of phase-locking in neurons with dendro-dendritic electrical coupling

Schwemmer

Lewis

2012

J. Math. Biol.

View full text Add to dashboard Cite

We examine the effects of dendritic filtering on the existence, stability, and robustness of phase-locked states to heterogeneity and noise in a pair of electrically coupled ball-and-stick neurons with passive dendrites. We use the theory of weakly coupled oscillators and analytically derived filtering properties of the dendritic coupling to systematically explore how the electrotonic length and diameter of dendrites can alter phase-locking. In the case of a fixed value of the coupling conductance (g c ) taken from the literature, we find that repeated exchanges in stability between the synchronous and anti-phase states can occur as the electrical coupling becomes more distally located on the dendrites. However, the robustness of the phase-locked states in this case decreases rapidly towards zero as the distance between the electrical coupling and the somata increases. Published estimates of g c are calculated from the experimentally measured coupling coefficient (CC) based on a single-compartment description of a neuron, and therefore may be severe underestimates of g c . With this in mind, we re-examine the stability and robustness of phase-locking using a fixed value of CC, which imposes a limit on the maximum distance the electrical coupling can be located away from the somata. In this case, although the phase-locked states remain robust over the entire range of possible coupling locations, no exchanges in stability with changing coupling position are observed except for a single exchange that occurs in the case of a high somatic firing frequency and a large dendritic radius. Thus, our analysis suggests that multiple exchanges in stability with changing coupling location are unlikely to be observed in real neural systems.

show abstract

“…This synchronization phenomenon does not require any signal exchanges or interactions between the oscillators for synchronization. The theory of this phenomenon has already been clarified for limit-cycle oscillators [2], [3]. Chaotic oscillators can also be synchronized by adding common noises [1].…”

Section: Introductionmentioning

confidence: 99%

Synchronization of Chaotic Oscillators Using Natural Environmental Noises

Hiroyuki

Hasegawa

2016

Journal of Signal Processing

View full text Add to dashboard Cite

In our research, we propose a novel synchronization scheme based on noise-induced synchronization. We introduce natural environmental noise as an additive input noise to uncoupled nonlinear oscillators. The natural environmental noises in neighboring areas are cross-correlated, and we have already shown that limit-cycle oscillators can be synchronized by such cross-correlated noise. In this paper, we investigate the feasibility of the proposed natural synchronization scheme for the Rössler system, one of the chaotic oscillators. We first evaluate the synchronization performance by adding cross-correlated Gaussian noise, and we show the possibility of synchronizing the chaotic oscillators using the crosscorrelated noise. We also introduce a real environmental noise, environmental sound data obtained at neighboring microphone devices, and we show that Rössler oscillators can be synchronized by such cross-correlated environmental noise. Our proposed synchronization method can be applied to intermittent communication. Accordingly, we evaluate the collision probability for the proposed synchronization method in intermittent communication. We introduce some cyclic interference sources and measure the probability of collision.

show abstract

Robustness of the Noise-Induced Phase Synchronization in a General Class of Limit Cycle Oscillators

Cited by 324 publications

References 30 publications

Spike-time reliability of layered neural oscillator networks

Spike-time reliability of layered neural oscillator networks

The robustness of phase-locking in neurons with dendro-dendritic electrical coupling

Synchronization of Chaotic Oscillators Using Natural Environmental Noises

Contact Info

Product

Resources

About