Spatial Coherence Resonance in Delayed Hodgkin–huxley Neuronal Networks

Abstract

We study the phenomenon of spatial coherence resonance (SCR) on Hodgkin–Huxley (HH) neuronal networks that are characterized with information transmission delay. In particular, we examine the ability of additive Gaussian noise to optimally extract a particular spatial frequency of excitatory waves in diffusive and small-world networks on which information transmission amongst directly connected neurons is not instantaneous. On diffusively coupled HH networks, we find that for short delay lengths, there always exists an intermediate noise level by which the noise-induced spatial dynamics is maximally ordered, hence implying the possibility of SCR in the system. Importantly thereby, the noise level warranting optimally ordered excitatory waves increases linearly with the increasing delay time, suggesting that extremely long delays might nevertheless preclude the observation of SCR on diffusive networks. Moreover, we find that the small-world topology introduces another obstacle for the emergence of ordered spatial dynamics out of noise because the magnitude of SCR fades progressively as the fraction of rewired links increases, hence evidencing decoherence of noise-induced spatial dynamics on delayed small-world HH networks. Presented results thus provide insights that could facilitate the understanding of the joint impact of noise and information transmission delay on realistic neuronal networks.

Improved Sensorimotor Performance via Stochastic Resonance

“…Synchronization subserves the selective and effective transmission of information in neuronal networks involved in sensorimotor integration (Fell and Axmacher, 2011;Siegel et al, 2012). The effects of noise on synchronization have also been explored in Hodgkin-Huxley neuronal networks (Wang et al, 2010) and other theoretical small-world networks (Perc, 2007(Perc, , 2008. In the somatosensory system, using afferent stimulation and simultaneously recording spinal and cortical evoked potentials in anesthetized cats, we reported that an intermediate level of tactile noise can enhance the coherence between the spinal and cortical evoked activity (Manjarrez et al, 2002b).…”

Diversity-induced resonance in the response to social norms

“…It was shown that there is an optimum level of the diversity (quenched noise) of the coupled units that maximizes the response to the signal. Subsequent works [4][5][6][7][8][9][10][11][12][13] showed that similar behavior can be observed in other physical systems, thus reinforcing the notion that this type of resonance can be a quite general phenomenon. In fact, diversity-induced resonance was also shown to appear in models related to sociophysics: It was found in discrete models of opinion formation [14] -such as the Galam model [15] (related to the randomfield Ising model at zero temperature [16]-and in continuous ones [17], of which the Deffuant model [18] is a paradigmatic example.…”

Adaptive stochastic resonance in self-organized small-world neuronal networks with time delay

“…It is shown that fine-tuned information transmission delays are vital for assuring optimally synchronized excitatory fronts on complex neuronal networks [25]. Moreover, resonance, as an indispensable part of neural dynamics, has also been widely investigated in delay-induced systems [28][29][30]. Researchers explored the SR in scale-free neuronal networks with transmission delay and found that multiple stochastic resonances can be induced by appropriately tuned delays irrespective to the placing of the subthreshold periodic pacemaker [31].…”