Regular Wave Propagation Out of Noise in Chemical Active Media

Alonso, Sergio; Sendiña‐Nadal, Irene; Pérez‐Muñuzuri, V.; Sancho, J. M.; Sagués, Francesc

doi:10.1103/physrevlett.87.078302

Cited by 96 publications

(42 citation statements)

References 27 publications

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“…These results are in Fig. 1 The domains of parameters D and I 0 for excitable and subexcitable systems agreement with those reported in references (Alonso et al 2002;Hou and Xin 2002). If we change the parameters, such that the coupling coefficient D = 0.063 and the external current I 0 = 5, the line wave cannot propagate with time, as shown in Fig.…”

Section: Model and Numerical Simulationsupporting

confidence: 88%

Noise-induced spatiotemporal patterns in Hodgkin–Huxley neuronal network

Liu

et al. 2013

Cogn Neurodyn

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The effect of noise on the pattern selection in a regular network of Hodgkin-Huxley neurons is investigated, and the transition of pattern in the network is measured from subexcitable to excitable media. Extensive numerical results confirm that kinds of travelling wave such as spiral wave, circle wave and target wave could be developed and kept alive in the subexcitable network due to the noise. In the case of excitable media under noise, the developed spiral wave and target wave could coexist and new target-like wave is induced near to the border of media. The averaged membrane potentials over all neurons in the network are calculated to detect the periodicity of the time series and the generated traveling wave. Furthermore, the firing probabilities of neurons in networks are also calculated to analyze the collective behavior of networks.

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Section: Model and Numerical Simulationsupporting

confidence: 88%

Noise-induced spatiotemporal patterns in Hodgkin–Huxley neuronal network

Liu

et al. 2013

Cogn Neurodyn

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“…For comparison, ͑aЈ͒ -͑dЈ͒ correspond to the noise-free case with a constant and uniform illumination fixed to the averaged intensity. From Alonso et al, 2001. Actually, the behavior shown in Fig. 37 constitutes a particular example of a whole range of noise-induced transitions linking different excitability regimes, including subexcitable→ excitable ͑the case of Fig.…”

Section: Excitability Transitions: Experimental and Numerical Realizamentioning

confidence: 99%

Spatiotemporal order out of noise

2007

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Natural systems are undeniably subject to random fluctuations, arising from either environmental variability or thermal effects. The consideration of those fluctuations supposes to deal with noisy quantities whose variance might at times be a sizable fraction of their mean levels. It is known that, under these conditions, noisy fluctuations can interact with the system's nonlinearities to render counterintuitive behavior, in which an increase in the noise level produces a more regular behavior. In systems with spatial degrees of freedom, this regularity takes the form of spatiotemporal order. An overview is presented of the mechanisms through which noise induces, enhances, and sustains ordered behavior in passive and active nonlinear media, and different spatiotemporal phenomena are described resulting from these effects. The general theoretical framework used in the analysis of these effects is reviewed, encompassing the theory of stochastic partial differential equations and coupled sets of ordinary stochastic differential equations. Experimental observations of self-organized behavior arising out of noise are also described, and details on the numerical algorithms needed in the computer simulation of these problems are given.

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“…Recently, it was observed that noise can support wave propagations in sub-excitable [20,17,15] systems due to a noise-induced transition [21,22]. In these studied, the medias are static, and transports are governed by diffusion [23].…”

Section: Introductionmentioning

confidence: 99%

Propagation of travelling waves in sub-excitable systems driven by noise and periodic forcing

Liu

Zhang

et al. 2007

Eur. Phys. J. B

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Abstract. It has been reported that traveling waves propagate periodically and stably in sub-excitable systems driven by noise [Phys. Rev. Lett. 88, 138301 (2002)]. As a further investigation, here we observe different types of traveling waves under different noises and periodic forces, using a simplified Oregonator model. Depending on different noises and periodic forces, we have observed different types of wave propagation (or their disappearance). Moreover, the reversal phenomena are observed in this system based on the numerical experiments in the one-dimensional space. As an explanation, we regard it as the effect of periodic forces. Thus, we give qualitative explanations to how reversal phenomena stably appear, which seem to arise from the mixing function of the periodic force and the noise. And the output period and three velocities (the normal, the positive and the negative) of the travelling waves are defined and their relationship with the periodic forces, along with the types of waves, are also studied in sub-excitable system under a fixed noise intensity.

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Regular Wave Propagation Out of Noise in Chemical Active Media

Cited by 96 publications

References 27 publications

Noise-induced spatiotemporal patterns in Hodgkin–Huxley neuronal network

Noise-induced spatiotemporal patterns in Hodgkin–Huxley neuronal network

Spatiotemporal order out of noise

Propagation of travelling waves in sub-excitable systems driven by noise and periodic forcing

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