Coherence resonance and discharge time reliability in neurons and neuronal models

Pakdaman, Khashayar; Tanabe, Seiji; Shimokawa, Tetsuya

doi:10.1016/s0893-6080(01)00025-9

Cited by 48 publications

(33 citation statements)

References 51 publications

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“…For the chosen parameters the FPT from x = 0 to x = x E can be split into two independent FPTs as T = T 1 +T 2 with T 1 being the FPT from x = 0 into the minimum x = a/b and T 2 being the time for the passage from the minimum to the absorbing boundary (see, for instance, ref. [42]). It is straightforward to show that…”

Section: B Escape Out Of a Parabolic Potential With Exponential Forcingmentioning

confidence: 99%

Moments of the First Passage Time Under External Driving

Lindner

2004

Journal of Statistical Physics

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A general theory is derived for the moments of the first passage time of a one-dimensional Markov process in presence of a weak time-dependent forcing. The linear corrections to the moments can be expressed by quadratures of the potential and of the time-dependent probability density of the unperturbed system or equivalently by its Laplace transform. If none of the latter functions is known, the derived formulas may still be useful for specific cases including a slow driving or a driving with power at only small or large times. In the second part of the paper, explicite expressions for mean and variance of the first passage time are derived for the cases of a linear or a parabolic potential and an exponentially decaying driving force. The analytical results are found to be in excellent agreement with computer simulations of the respective first-passage processes.The particular examples furthermore demonstrate that already the effect of a simple exponential driving can be fairly involved implying a nontrivial nonmonotonous behavior of mean and variance as functions of the driving's time scale.

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Section: B Escape Out Of a Parabolic Potential With Exponential Forcingmentioning

confidence: 99%

Moments of the First Passage Time Under External Driving

Lindner

2004

Journal of Statistical Physics

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“…C x 1 ;x 2 is the area under the curve of the power spectrum within a certain range of frequency, which measures the peak of the power spectrum. Coherence, used commonly in the field of stochastic nonlinear dynamics, could quantify the sharpness of the peak in the spike train power spectral density (Lindner et al 2002;Pakdaman et al 2001). …”

Section: Model and Numerical Methodsmentioning

confidence: 99%

Effect of inhibitory feedback on correlated firing of spiking neural network

Xie

Wang

2013

Cogn Neurodyn

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Understanding the properties and mechanisms that generate different forms of correlation is critical for determining their role in cortical processing. Researches on retina, visual cortex, sensory cortex, and computational model have suggested that fast correlation with high temporal precision appears consistent with common input, and correlation on a slow time scale likely involves feedback. Based on feedback spiking neural network model, we investigate the role of inhibitory feedback in shaping correlations on a time scale of 100 ms. Notably, the relationship between the correlation coefficient and inhibitory feedback strength is non-monotonic. Further, computational simulations show how firing rate and oscillatory activity form the basis of the mechanisms underlying this relationship. When the mean firing rate holds unvaried, the correlation coefficient increases monotonically with inhibitory feedback, but the correlation coefficient keeps decreasing when the network has no oscillatory activity. Our findings reveal that two opposing effects of the inhibitory feedback on the firing activity of the network contribute to the non-monotonic relationship between the correlation coefficient and the strength of the inhibitory feedback. The inhibitory feedback affects the correlated firing activity by modulating the intensity and regularity of the spike trains. Finally, the non-monotonic relationship is replicated with varying transmission delay and different spatial network structure, demonstrating the universality of the results.

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“…The stochastic HH equations define an ergodic random dynamical system. The solutions of these equations tend to a stationary stochastic process after a transient time (Pakdaman and Tanabe 2001). The time-and frequency-domain measures depicted in the following sections characterize the properties of this process.…”

Section: Stochastic Hodgkin-huxley Equationsmentioning

confidence: 99%

“…Furthermore, we showed that this transition could have implications in neuronal coding because it separated the regimes where noise increased the sensitivity of neurons from the ones where noise reduced it. In this way, the noise-induced transition plays a pivotal role in the potentially beneficial effects of noise, such as enhanced discharge-time precision and reliability (Pakdaman et al 2001;Tanabe and Pakdaman 2001b).…”

Section: Introductionmentioning

confidence: 99%

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White-noise stimulation of the Hodgkin-Huxley model

Takahata

Tanabe

Pakdaman

2002

Biological Cybernetics

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We studied the combined influence of noise and constant current stimulations on the Hodgkin-Huxley neuron model through time and frequency analysis of the membrane-potential dynamics. We observed that, in agreement with experimental data (Guttman et al. 1974), at low noise and low constant current stimulation the behavior of the model is well approximated by that of the linearized Hodgkin-Huxley system. Conversely, nonlinearities due to firing dominate at large noise or current stimulations. The transition between the two regimes is abrupt, and takes place in the same range of noise and current intensities as the noise-induced transition characterized by the qualitative change in the stationary distribution of the membrane potential (Tanabe and Pakdaman 2001a). The implications of these results are discussed.

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Coherence resonance and discharge time reliability in neurons and neuronal models

Cited by 48 publications

References 51 publications

Moments of the First Passage Time Under External Driving

Moments of the First Passage Time Under External Driving

Effect of inhibitory feedback on correlated firing of spiking neural network

White-noise stimulation of the Hodgkin-Huxley model

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