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Predicting the coherence resonance curve using a semianalytical treatment
Santidan Biswas1, Dibyendu Das, P Parmananda
1Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai, India. santidan@phy.iitb.ac.in
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2009
Summary
Noise can surprisingly create regular patterns in nonlinear systems. This study explains why the normalized variance of spike timing shows a single peak, offering a general formula validated by models.
Area of Science:
- Nonlinear dynamics
- Computational neuroscience
- Chemical kinetics
Background:
- Noise-induced regularity, or coherence resonance, is a known phenomenon in nonlinear excitable systems.
- The normalized variance of interspike time intervals (V(N)) quantifies the regularity of spiking activity.
Purpose of the Study:
- To theoretically explain the unimodal profile of V(N) in nonlinear excitable systems.
- To derive a general formula for V(N) that characterizes the noise-induced regularity.
Main Methods:
- A semianalytic treatment of the spiking process associated with nonlinear excitable systems.
- Numerical simulations using the FitzHugh-Nagumo model and a chemical oscillator model as test cases.
Main Results:
- A general and simple formula for V(N) was derived, explaining its unimodal behavior.
- The derived formula showed excellent agreement with numerical results from both test models.
- The study provides a theoretical framework for understanding noise-induced regularity.
Conclusions:
- The theoretical explanation for the unimodal profile of V(N) is robust.
- The derived formula offers a valuable tool for analyzing regularity in various nonlinear excitable systems.
- This work deepens the understanding of coherence resonance and its underlying mechanisms.
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