Array-enhanced coherence resonance and forced dynamics in coupled FitzHugh-Nagumo neurons with noise

Abstract

Nonlinear dynamics of coupled FitzHugh-Nagumo neurons subject to independent noise is analyzed. A kind of self-sustained global oscillation with almost synchronous firing is generated by array-enhanced coherence resonance. Further, forced dynamics of the self-sustained global oscillation stimulated by sinusoidal input is analyzed and classified as synchronized, quasiperiodic, and chaotic responses just like the forced oscillations in nerve membranes observed by in vitro experiments with squid giant axons. Possible physiological importance of such forced oscillations is also discussed.

Noise induced complexity: From subthreshold oscillations to spiking in coupled excitable systems

“…Despite its relative simplicity it displays a variety of biologically relevant dynamical regimes if taken as a single element or embedded into a network. It has been shown that the influence of noise on excitable systems such as the FitzHugh-Nagumo model can lead to a coherent temporal response via the phenomena of stochastic [1] and coherence [22,36,37] resonance.…”

Coherence Resonance in Coupled Theta Neurons

“…Synchronization of two coupled CR oscillators was also studied numerically and experimentally [12]. Furthermore, array-enhanced CR was found to occur via noise-induced synchronization in globally coupled Hodgkin-Huxley neurons [13] and in locally coupled FitzHugh-Nagumo neurons [14,15]. In this paper, we are interested in the dynamical response of an individual neuron to noise in a large excitatory network of globally coupled neurons with type-I excitability and study how such a response within the network differs from that of an isolated type-I neuron.…”

“…This weak CR is in contrast to the "strong" CR, occurring for a type-II neuron, where a maximal correlation occurs along with the spectral CR. To our knowledge, only networks consisting of neurons exhibiting strong CR (e.g., Hodgkin-Huxley [13] and FitzHughNagumo [14,15] neurons) were considered in previous studies on the CR. We note that most mammalian neurons are known to exhibit type-I excitability [22].…”

Detecting chaotic structures in noisy pulse trains based on interspike interval reconstruction

“…In such a system, an interspike interval sequence is thought to give some information about the neuronal networks, and the reconstruction of the dynamical system from the interspike interval sequences was performed by several authors (Theiler et al 1992;Sauer 1994;Suzuki et al 2000;Shinohara et al 2002). Also in such a Correspondence to: T. Kanamaru (e-mail: kanamaru@sekine-lab.ei.tuat.ac.jp) situation, the effects of noise often lead to wrong results, so careful treatments would be required.…”

“…In the present paper, the nonlinear prediction method (Theiler et al 1992;Sauer 1994;Suzuki et al 2000;Shinohara et al 2002) based on the interspike interval (ISI) reconstruction is applied to noisy pulse trains, and the detection of the deterministic structure is performed in order to establish a method for the detection of chaotic structures in noisy pulse trains. Based on those results, the dynamical states of the system are discriminated.…”