Spatial coherence resonance in excitable media

2005 ◽  
Vol 72 (1) ◽  
Author(s):  
Matjaž Perc
Keyword(s):  
Spatial Coherence ◽  
Excitable Media ◽  
Coherence Resonance

Stochastic Signal Induced Multiple Spatial Coherence Resonances and Spiral Waves in Excitable Media

2009 ◽  
Vol 26 (3) ◽  
pp. 030504 ◽  
Author(s):  
Li Yu-Ye ◽  
Zhang Hui-Min ◽  
Wei Chun-Ling ◽  
Yang Ming-Hao ◽  
Gu Hua-Guang ◽  
...  
Keyword(s):  
Spatial Coherence ◽  
Spiral Waves ◽  
Excitable Media ◽  
Stochastic Signal

scholarly journals Spatial coherence resonance near pattern-forming instabilities

2004 ◽  
Vol 65 (4) ◽  
pp. 452-458 ◽  
Author(s):  
O Carrillo ◽  
M. A Santos ◽  
J García-Ojalvo ◽  
J. M Sancho
Keyword(s):  
Spatial Coherence ◽  
Coherence Resonance ◽  
Pattern Forming

The Influence of Initial Values on Spatial Coherence Resonance in a Neuronal Network

2015 ◽  
Vol 25 (08) ◽  
pp. 1550104 ◽  
Author(s):  
Yuye Li ◽  
Huaguang Gu
Keyword(s):  
Membrane Potential ◽  
Residence Time ◽  
Resting State ◽  
Spatial Coherence ◽  
Low Noise ◽  
Stable Node ◽  
Stable Limit ◽  
Coherence Resonance ◽  
Initial Values ◽  
Unstable Focus

Noise-induced single spatial coherence resonance (CR) and multiple spatial CRs simulated in a network have been reported independently in previous studies. In this paper, the relationship between the single and multiple spatial CRs is established by adjusting the initial values of the network composed of Morris–Lecar (ML) model neurons. The ML model manifests a saddle-node bifurcation on an invariant cycle through which a resting state is changed to a stable limit cycle corresponding to period-1 firing. Under resting state, a stable node, a saddle, and an unstable focus coexist. The membrane potential of the unstable focus is much higher than that of the stable node. When the initial value is closer to the unstable focus, the residence time of membrane potential on a high level is longer; correspondingly, the spatial CRs appear more frequently with respect to noise intensity and the coherence degree becomes stronger. The single spatial CR is induced by noise with high intensity. Multiple spatial CRs are induced by noise with high, middle, and even low noise intensities, respectively. When the initial values are closer to an unstable focus, the residence time of membrane potentials on a higher level is longer, which is important to the generation of multiple CRs, and builds a relationship between single and multiple spatial CRs.

Spatial coherence resonance and spatial pattern transition induced by the decrease of inhibitory effect in a neuronal network

2017 ◽  
Vol 31 (26) ◽  
pp. 1750179 ◽  
Author(s):  
Ye Tao ◽  
Huaguang Gu ◽  
Xueli Ding
Keyword(s):  
Spatial Patterns ◽  
Neuronal Network ◽  
Brain Cortex ◽  
Pyramidal Neurons ◽  
Spatial Coherence ◽  
Inhibitory Effect ◽  
Spiral Waves ◽  
Inhibitory Interneurons ◽  
Coherence Resonance ◽  
Biological Experiment

Spiral waves were observed in the biological experiment on rat brain cortex with the application of carbachol and bicuculline which can block inhibitory coupling from interneurons to pyramidal neurons. To simulate the experimental spiral waves, a two-dimensional neuronal network composed of pyramidal neurons and inhibitory interneurons was built. By decreasing the percentage of active inhibitory interneurons, the random-like spatial patterns change to spiral waves and to random-like spatial patterns or nearly synchronous behaviors. The spiral waves appear at a low percentage of inhibitory interneurons, which matches the experimental condition that inhibitory couplings of the interneurons were blocked. The spiral waves exhibit a higher order or signal-to-noise ratio (SNR) characterized by spatial structure function than both random-like spatial patterns and nearly synchronous behaviors, which shows that changes of the percentage of active inhibitory interneurons can induce spatial coherence resonance-like behaviors. In addition, the relationship between the coherence degree and the spatial structures of the spiral waves is identified. The results not only present a possible and reasonable interpretation to the spiral waves observed in the biological experiment on the brain cortex with disinhibition, but also reveal that the spiral waves exhibit more ordered degree in spatial patterns.

SPATIAL COHERENCE RESONANCE IN DELAYED HODGKIN–HUXLEY NEURONAL NETWORKS

2010 ◽  
Vol 24 (09) ◽  
pp. 1201-1213 ◽  
Author(s):  
QING YUN WANG ◽  
MATJAŽ PERC ◽  
ZHI SHENG DUAN ◽  
GUAN RONG CHEN
Keyword(s):  
Information Transmission ◽  
Noise Level ◽  
Neuronal Networks ◽  
Spatial Coherence ◽  
Spatial Dynamics ◽  
Small World ◽  
Transmission Delay ◽  
Small World Networks ◽  
Coherence Resonance ◽  
Short Delay

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.

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