Clustering of noise-induced oscillations

Abstract

The subject of our study is clustering in a population of excitable systems driven by Gaussian white noise and with randomly distributed coupling strength. The cluster state is frequency-locked state in which all functional units run at the same noise-induced frequency. Cooperative dynamics of this regime is described in terms of effective synchronization and noise-induced coherence.

Revealing direction of coupling between neuronal oscillators from time series: Phase dynamics modeling versus partial directed coherence

“…However, subsequent ISI values may have the least variance for some intermediate noise level so that the dynamics are similar to a moderately perturbed periodic spiking. [33][34][35] Such an effect is called "coherence resonance." 33 The other possible type of neuron dynamics is called "bursting" ͑see, e.g., Refs.…”

Patterned Brain Stimulation, What a Framework with Rhythmic and Noisy Components Might Tell Us about Recovery Maximization

“…Conjecturing that the brain is a system utilizing distinct frequencies from null to above 200 Hz as possible communication channels and that the selection of “active” channels is done via phase-locking, the question is which mechanism putatively acts as the “switch”? To put it more blatantly: could neural noise (in the notion of a complex, not understood, and non-random mechanism) act as the controller of communications in the brain (Horsthemke and Lefever, 1984; Neiman et al, 1999; Sosnovtseva et al, 2001; Misic et al, 2010)?…”

“…It has been shown that noise: (i) can “switch” between these states (Neiman et al, 1999; Bascones et al, 2002; Misic et al, 2010), (ii) induces oscillations itself (Zhou et al, 2003; Ermentrout et al, 2008; Ghosh et al, 2008), and (iii) enhances phase synchronization (Neiman et al, 1999) as well as de-synchronization (Kurrer and Schulten, 1995). When considering realistically large coupled excitable systems of model neurons, the presence of noise leads to a clustering of frequencies (Postnov et al, 2001; Sosnovtseva et al, 2001; Brunel and Hansel, 2006; Deco et al, 2009), i.e., neurons form groups characterized by (almost) the same “stochastic eigenfrequency.” The number of such clusters strongly depends on the distribution interval of coupling, the larger the coupling the less clusters form. Interestingly a relaxed notion of phase-locking is sufficient for this phenomenon to occur (Sosnovtseva et al, 2001).…”

“…When considering realistically large coupled excitable systems of model neurons, the presence of noise leads to a clustering of frequencies (Postnov et al, 2001; Sosnovtseva et al, 2001; Brunel and Hansel, 2006; Deco et al, 2009), i.e., neurons form groups characterized by (almost) the same “stochastic eigenfrequency.” The number of such clusters strongly depends on the distribution interval of coupling, the larger the coupling the less clusters form. Interestingly a relaxed notion of phase-locking is sufficient for this phenomenon to occur (Sosnovtseva et al, 2001). Kurrer and Schulten (1995) have shown, that the role of noise in a system of coupled excitable systems is twofold: in the low-noise transition, noise induces synchronicity, while in the high-noise transition it leads to a loss of coherency (de-synchronization), following a sigmoid transition function between synchronization and de-synchronization.…”

Spatiotemporal order out of noise

“…Disorder as a source of oscillations has been also considered ͑Cartwright, 2000; Boschi et al, 2001;Sosnovtseva et al, 2001͒. Diversity is claimed to provoke emergence of global oscillations from individual quiescent elements in heterogeneous excitable media.…”