Quantitative measures of stochastic resonance effect based on switch-phase distribution.

Area of Science:

• Complex Systems
• Nonlinear Dynamics
• Signal Processing

Background:

• Stochastic resonance (SR) is a phenomenon where noise enhances signal detection in nonlinear systems.
• Traditional SR quantification relies on complex power spectral measures requiring extensive data.
• A need exists for simpler, more accessible methods to characterize SR.

Purpose of the Study:

• To propose novel, practical measures for characterizing the stochastic resonance effect.
• To validate these measures using experimental data from Chua's circuit.
• To explore the potential applications of these new metrics.

Main Methods:

• Development of two switch-phase distribution-based measures: power norm and probability within a specific phase range.
• Experimental implementation in Chua's circuit operating in a chaotic regime.
• Analysis of switch-phase distributions under varying Gaussian noise intensities.

Main Results:

• The proposed measures accurately identify the optimal noise level for SR, consistent with the signal-to-noise ratio (SNR).
• The power norm measure shows similar noise intensity dependence as SNR.
• The second measure exhibits a unique dependence on noise intensity, with an inflection point at optimal noise.

Conclusions:

• The new switch-phase distribution measures offer a simpler and practical alternative for SR detection.
• These metrics are effective in experimental settings, demonstrated in Chua's circuit.
• The proposed measures hold promise for applications in adaptive SR and signal processing, including aperiodic signal coding and decoding.