# American Institute of Mathematical Sciences

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2006, 3(4): 583-602. doi: 10.3934/mbe.2006.3.583

## Noise-sensitive measure for stochastic resonance in biological oscillators

 1 School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287-5706 2 Department of Electrical Engineering, Arizona State University, Tempe, AZ 85287, United States

Received  February 2006 Revised  March 2006 Published  August 2006

There has been ample experimental evidence that a variety of biological systems use the mechanism of stochastic resonance for tasks such as prey capture and sensory information processing. Traditional quantities for the characterization of stochastic resonance, such as the signal-to-noise ratio, possess a low noise sensitivity in the sense that they vary slowly about the optimal noise level. To tune to this level for improved system performance in a noisy environment, a high sensitivity to noise is required. Here we show that, when the resonance is understood as a manifestation of phase synchronization, the average synchronization time between the input and the output signal has an extremely high sensitivity in that it exhibits a cusp-like behavior about the optimal noise level. We use a class of biological oscillators to demonstrate this phenomenon, and provide a theoretical analysis to establish its generality. Whether a biological system actually takes advantage of phase synchronization and the cusp-like behavior to tune to optimal noise level presents an interesting issue of further theoretical and experimental research.
Citation: Ying-Cheng Lai, Kwangho Park. Noise-sensitive measure for stochastic resonance in biological oscillators. Mathematical Biosciences & Engineering, 2006, 3 (4) : 583-602. doi: 10.3934/mbe.2006.3.583
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