High-frequency effects in the FitzHugh-Nagumo neuron model

Abstract

The effect of a high-frequency signal on the FitzHugh-Nagumo excitable model is analyzed. We show that the firing rate is diminished as the ratio of the high-frequency amplitude to its frequency is increased. Moreover, it is demonstrated that the excitable character of the system, and consequently the firing activity, is suppressed for ratios above a given threshold value. In addition, we show that the vibrational resonance phenomenon turns up for sufficiently large noise strength values. DOI: 10.1103/PhysRevE.73.061102 PACS number͑s͒: 05.40.Ϫa, 02.50.Ϫr, 87.19.La, 05.90.ϩm Nonlinear noisy systems have been studied with ever growing interest due to the applicability to the modeling of a great variety of phenomena of relevance in physics, chemistry, and the life sciences ͓1,2͔. Perhaps, the simplest nonlinear noisy system studied in the literature is the bistable system, which has been used successfully to illustrate the phenomenon of stochastic resonance. In addition, the spiking activity of a neuron has been theoretically studied using nonlinear excitable noisy models ͓3͔, among them, the FitzHugh-Nagumo ͑FHN͒ system ͓4͔ being one of the most utilized due to its simplicity. Besides, networks of FHN units have been considered as simplified models useful in the description of both the cardiac tissue ͓5-8͔ and reactiondiffusion chemical systems ͓9,8͔.Recently, it has been shown, both theoretically and experimentally, that the addition of a high-frequency ͑HF͒ signal results in an improvement of the stochastic resonance in a bistable optical system ͓10͔. Nevertheless, many experimental studies have suggested that HF ͑nonionizing͒ fields may damage several structural and functional properties of neuronal membranes in single cells, as well as cause a number of negative physiological effects on typically excitable media such as cardiac tissue ͓11͔. It has also been found that certain HF signals are able to suppress the steady directed motion in a ratchet model ͓12͔. Thus, HF signals seem to play a twofold role, positive or negative, depending on the nonlinear system under consideration.In this paper we study the influence of a HF field on a rather simple excitable model, such as the archetypal FHN system. This system is governed by the following equations ͓13͔:In the context of neurophysiology, v͑t͒ is called the voltage variable, and w͑t͒ the recovery variable. Here S͑t͒ is an external forcing of period T, ͑t͒ a noisy term, and ⌫͑t͒ is an added HF signal which will be specified later on. The "neuronal" noise ͑t͒ is assumed to be an unbiased Gaussian white noise with the autocorrelation function ͗͑t͒͑s͒͘ =2D␦͑t − s͒. The values of the model parameters define the dynamical regimes of the system, and are discussed below. Let us focus our attention on the deterministic FHN model ͑D =0͒ in the absence of a HF signal ͓⌫͑t͒ =0͔. In the case of a time-independent external signal S͑t͒ = S 0 , the excitable character of the FHN model relies on the existence of a threshold value of this signal, S H , at which a Hopf bifurca...

Stochastic resonance with weak monochromatic driving: Gains above unity induced by high-frequency signals

“…2, we have also plotted with solid line the SR gain obtained from the numerical solution of the effective dynamics in eq. (12). A glance at that figure reveals that the agreement between both dynamics is excellent for N = 4000.…”

“…However, as mentioned in the same reference, this positive effect of the HF force seems to be absent when the signal of interest is sinusoidal. It is pertinent to point out that the effect of HF fields on nonlinear stochastic systems is not necessarily positive (see, for instance, [11] for a ratchet p-1 model and [12] for an excitable model). Nevertheless, in ratchet models positive effects have been also found [13].…”

“…In order to reduce the effective Langevin equation [eq. (12)] to the standard form [eq. (1)], it is convenient to introduce the following time and space scale changes:…”

Influence of strong noise on the decline and propagation of population in the delayed Malthus–Verhulst model

“…Zhang and Yao found noise-induced intermittency in two-dimensional Hamiltonian systems with strong noise [11]. The appearance of self-replicating patterns controlled by noise in a stochastic reaction-diffusion model was described [12] by Lesmes et al Cubero et al showed that a vibrational resonance phenomenon turns up in the FitzHugh-Nagumo neuron model for sufficiently large noise strength values [13]. Seo et al studied a two-state system under time-periodic perturbations in the large-noise region by Monte-Carlo simulations [14].…”

Subthreshold Periodic Signal Detection by Bounded Noise-Induced Resonance in the FitzHugh–Nagumo Neuron

“…This phenomenon is called vibrational resonance (VR) [14]. It should be mentioned 2 Complexity that two-frequency driving systems can be found in many different fields, such as the communication field where HF carrier waves are usually used to enhance the target signal [13], neuroscience [15], acoustics [16], and laser physics [17]. The influences of VR on signal detection and amplification have been widely investigated in these systems subjected to LF and HF driving forces.…”