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Coherence and Stochastic Resonances in Fhn Model

In: Science

Submitted By pratikta16
Words 744
Pages 3
Coherence and Stochastic Resonance of FHN Model

1

Introduction

Deterministic, nonlinear systems with excitable dynamics, e.g. the FitzHugh Nagumo (FHN) Model, undergo bifurcation from stable focus to limit cycle on tuning the system parameter. However, addition of uncorrelated noise to the system can kick the system to the limit cycle region, thus exhibiting spiking behaviour if the parameter is hold on the fixed point side. Thus the system exhibits intermittent cyclic behaviour, manifesting as spikes in the dynamical variable. It is interenting to note that at an optimal value of noise, the seemingly irregular behaviour of the spikes becomes strangely regular. The interspike interval τp becomes almost regular and the Normal√ p ized Variance of the interspike interval, defined by VN = exhibits τp a minima as a function of noise strength (D). The phenomenon is termed as Coherence Resonance. Coherence Resonance is a system generated response to the noise. However, there is another form of resonance that is found at lower level of noise in response to a subthreshold signal, known as Stochastic Resonance. Subthreshold signals that are in general undetectable can often be detected in presence of noise. There is an optimal level of noise at which such information transmission is optimal. Stochastic resonance has been investigated in many physical, chemical and biological systems. It can be utilised for enhancing signal detection and information transfer. SR has been obversed for subthreshold input signals of both periodic as well as aperiodic types. The former is known as Periodic Stochastic Resonance (PSR), while the later is known as Aperiodic Stochastic Resonance (ASR). In PSR, normalized variance of the output signal is found to reach a minima at an optimal level of noise, which is the signature of optimal information transmission. In ASR, the cross-correlation...

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