Bursting behaviour of the FitzHugh-Nagumo neuron model subject to quasi-monochromatic noise

Baltanás, J. P.; Casado, José Manuel Ribera

doi:10.1016/s0167-2789(98)00176-6

Cited by 34 publications

(31 citation statements)

References 13 publications

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“…Several basic models have been considered to demonstrate CR (or ASR) in neuronal firings theoretically" such as the FitzHugh-Nagumo (FHN) model [124], the HR model [125] and the Plant model [126] and others [40,41,127]. In two major classes of bursting neuron models (the Plant and HR models), noise makes the output firing patterns sensitive to the characteristics of autonomous subthreshold oscillations in the absence of periodic input.…”

Section: Stochastic and Coherence Resonances In Neuronal Firingsmentioning

confidence: 99%

“…An example of CR in the FHN model was shown in [127]. For weak noise the output spike train looks random, and interspike intervals (ISIs) varies substantially.…”

Section: Stochastic and Coherence Resonances In Neuronal Firingsmentioning

confidence: 99%

“…It is a crucial point for obtaining the skipping that the deterministic dynamics must be subthreshold. Stochastic models of the firing patterns without periodic forcing were briefly mentioned in [55,127,129,[136][137][138][139], and it was further pointed out that the dynamical behavior of skipping or stochastic phaselocking might exhibit before a supercritical or subcritical Hopf bifurcation in the corresponding deterministic models. In two major classes of bursting neuron models (the Plant and HR models), the focus was on the sensitivity of firing pattern to noise and to the bifurcation leading to subthreshold dynamics [41].…”

Section: Noise-induced "Skippings" or Integer Multiple Firing Patternsmentioning

confidence: 99%

“…In two major classes of bursting neuron models (the Plant and HR models), the focus was on the sensitivity of firing pattern to noise and to the bifurcation leading to subthreshold dynamics [41]. QMN could give rise to spontaneous bursting in the subthreshold regime of the FHN system corresponding to the stable fixed point [127]. Moreover, it was found that QMN drove the system to fire preferentially at a given phase of its central frequency, but bursts were separated in a random integer number of the period of oscillation.…”

Section: Noise-induced "Skippings" or Integer Multiple Firing Patternsmentioning

confidence: 99%

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Dynamics of firing patterns, synchronization and resonances in neuronal electrical activities: experiments and analysis

Yang

et al. 2008

Acta Mech Sin

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Recent advances in the experimental and theoretical study of dynamics of neuronal electrical firing activities are reviewed. Firstly, some experimental phenomena of neuronal irregular firing patterns, especially chaotic and stochastic firing patterns, are presented, and practical nonlinear time analysis methods are introduced to distinguish deterministic and stochastic mechanism in time series. Secondly, the dynamics of electrical firing activities in a single neuron is concerned, namely, fast-slow dynamics analysis for classification and mechanism of various bursting patterns, one-or two-parameter bifurcation analysis for transitions of firing patterns, and stochastic dynamics of firing activities (stochastic and coherence resonances, integer multiple and other firing patterns induced by noise, etc.).types of synchronization of coupled neurons with electrical and chemical synapses are discussed. As noise and time delay are inevitable in nervous systems, it is found that noise and time delay may induce or enhance synchronization and change firing patterns of coupled neurons. Noise-induced resonance and spatiotemporal patterns in coupled neuronal networks are also demonstrated. Finally, some prospects are presented for future research. In consequence, the idea and methods of nonlinear dynamics are of great significance in exploration of dynamic processes and physiological functions of nervous systems.

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Section: Stochastic and Coherence Resonances In Neuronal Firingsmentioning

confidence: 99%

“…An example of CR in the FHN model was shown in [127]. For weak noise the output spike train looks random, and interspike intervals (ISIs) varies substantially.…”

Section: Stochastic and Coherence Resonances In Neuronal Firingsmentioning

confidence: 99%

Section: Noise-induced "Skippings" or Integer Multiple Firing Patternsmentioning

confidence: 99%

Section: Noise-induced "Skippings" or Integer Multiple Firing Patternsmentioning

confidence: 99%

See 2 more Smart Citations

Dynamics of firing patterns, synchronization and resonances in neuronal electrical activities: experiments and analysis

Yang

et al. 2008

Acta Mech Sin

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show abstract

“…Recently, analysis has focused on a dynamic cellular response to a signal that is controlled externally by a parameter (Sauer, 1994;Baltanas and Casado, 1998). A great deal of research has been performed to decode this signal from spikes, or action potentials, in voltage time series.…”

Section: Introductionmentioning

confidence: 99%