Modeling noise induced resonance in an excitable system: An alternative approach

TL;DR

This paper introduces a new modeling approach to explain noise-induced resonance phenomena in excitable systems, including coherence resonance, stochastic resonance, and constant coherence resonance, by focusing on noise's perturbative effect on system parameters.

Contribution

It proposes a general model that captures multiple noise-induced resonance phenomena through a mechanism where noise perturbs control parameters without destructive interference.

Findings

Successfully models coherence resonance, stochastic resonance, and CCR.

Explains frequency shifts in CCR with noise level.

Demonstrates noise perturbation as a key factor in resonance phenomena.

Abstract

Recently, it is observed [Md. Nurujjaman et al, Phy. Rev. E \textbf{80}, 015201 (R) (2009)] that in an excitable system, one can maintain noise induced coherency in the coherence resonance by blocking the destructive effect of the noise on the system at higher noise level. This phenomenon of constant coherence resonance (CCR) cannot be explained by the existing way of simulation of the model equations of an excitable system with added noise. In this paper, we have proposed a general model which explains the noise induced resonance phenomenon CCR as well as coherence resonance (CR) and stochastic resonance (SR). The simulation has been carried out considering the basic mechanism of noise induced resonance phenomena: noise only perturbs the system control parameter to excite coherent oscillations, taking proper precautions so that the destructive effect of noise does not affect the system. In this approach, the CR has been obtained from the interference between the system output and noise, and the SR has been obtained by adding noise and a subthreshold signal. This also explains the observation of the frequency shift of coherent oscillations in the CCR with noise level.