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Chaos pass filter: linear response of synchronized chaotic systems
Steffen Zeeb1, Johannes Kestler, Ido Kanter
1Institute of Theoretical Physics, University of Würzburg, Am Hubland, 97074 Würzburg, Germany. steffen.zeeb@physik.uni-wuerzburg.de
Summary
Synchronized chaotic systems can filter external noise, acting as a chaos pass filter. This noise filtering capability is analyzed using distance distributions and bit error rates, revealing complex behaviors and potential for complete perturbation removal.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Information Theory
Background:
- Investigating the linear response of synchronized chaotic systems to external perturbations is crucial for understanding noise filtering.
- The phenomenon of chaos pass filter in iterated maps with time delays requires detailed analysis.
Purpose of the Study:
- To analyze the linear response of synchronized time-delayed chaotic systems to external perturbations.
- To quantify this response using distance distributions and bit error rates.
- To explore the impact of model parameters and system architecture on noise filtering.
Main Methods:
- Numerical and analytical calculations of distance distributions between synchronized chaotic units.
- Quantification of linear response via bit error rate analysis.
- Investigation of harmonic perturbations and system configurations like bidirectionally coupled chains.
Main Results:
- Distance distributions exhibit power-law tails in the synchronization region, leading to diverging moments.
- Bit error rate shows complex nonmonotonic behavior and can exhibit a devil's staircase structure.
- Resonances are observed in response to harmonic perturbations, dependent on coupling and delay times.
Conclusions:
- Synchronized chaotic systems can effectively filter external perturbations.
- System parameters and coupling configurations significantly influence the filtering performance.
- A bidirectionally coupled chain of three units can achieve complete perturbation filtering, zeroing the bit error rate.
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