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Published on: November 11, 2013
Memory-enhanced energetic stability for a fractional oscillator with fluctuating frequency
1Institute of Mathematics and Natural Sciences, Tallinn University, 25 Narva Road, 10120 Tallinn, Estonia.
Summary
This study examines a fractional oscillator with fluctuating frequency, revealing that intermediate memory effects enhance its stability and signal-to-noise ratio (SNR). This memory-induced stability is key for understanding complex system dynamics.
Area of Science:
- Nonlinear Dynamics
- Statistical Physics
- Complex Systems
Background:
- Fractional oscillators exhibit complex behaviors influenced by memory effects.
- Fluctuating environments introduce noise, impacting system dynamics and signal characteristics.
Purpose of the Study:
- Investigate the long-time limit behavior of variance and correlation functions for a fractional oscillator.
- Analyze the impact of fluctuating eigenfrequency and viscoelastic friction with memory on system stability and stochastic resonance (SR).
Main Methods:
- Modeling the environment using multiplicative and additive white noise.
- Assuming a power-law function for the viscoelastic friction kernel with memory.
- Calculating exact expressions for stochastic resonance characteristics (variance, SNR).
Main Results:
- Intermediate memory exponent values significantly enhance the oscillator's energetic stability.
- A multiresonance-like behavior of variance and SNR was observed as a function of the memory exponent.
- Established a link between memory-induced stability and the observed multiresonance effect.
Conclusions:
- Memory effects play a crucial role in enhancing the energetic stability of fractional oscillators.
- The findings are relevant for understanding systems with viscoelasticity and fluctuating parameters, even without harmonic potentials.
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