Noise-sensitive measure for stochastic resonance in biological oscillators
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1.
School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287-5706
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2.
Department of Electrical Engineering, Arizona State University, Tempe, AZ 85287
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Received:
01 February 2006
Accepted:
29 June 2018
Published:
01 August 2006
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MSC :
37H10, 92B99.
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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[J]. Mathematical Biosciences and Engineering, 2006, 3(4): 583-602. doi: 10.3934/mbe.2006.3.583
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Abstract
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.
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