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Multifractal characterization of stochastic resonance
1Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan.
Summary
This study introduces a new multifractal measure to quantify stochastic resonance and system complexity. The singularity spectrum effectively detects stochastic resonance and synchronization, even in short data sequences.
Area of Science:
- Nonlinear Dynamics
- Complex Systems Analysis
- Statistical Physics
Background:
- Stochastic resonance (SR) enhances weak signals in noisy nonlinear systems.
- Characterizing the complex dynamics of bistable systems is crucial.
- Existing measures may not fully capture system complexity under various inputs.
Purpose of the Study:
- To introduce a novel multifractal measure for characterizing stochastic resonance.
- To assess the efficacy of this measure for quantifying system complexity.
- To explore its application in periodic, aperiodic, and coupled neuron systems.
Main Methods:
- Application of a multifractal formalism.
- Calculation of a singularity spectrum from return time sequences.
- Utilizing the wavelet transform modulus maxima method.
Main Results:
- The width of the singularity spectrum quantifies complexity for diverse input signals.
- Multifractality transitions to monofractality during stochastic synchronization.
- The measure detects stochastic resonance even in short time series data.
Conclusions:
- The degree of multifractality serves as a robust complexity and synchronization measure.
- This approach offers a new perspective on stochastic resonance detection.
- The method is applicable to coupled stochastic neuron dynamics.