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Power-law persistence characterizes traveling waves in coupled circle maps with repulsive coupling
Prashant M Gade1, D V Senthilkumar, Sukratu Barve
1Centre for Modeling and Simulation, University of Pune, Pune 411 007, India.
Summary
Persistence analysis effectively characterizes states in coupled circle maps. Repulsive coupling reveals power-law decay in traveling waves across the entire phase, explained by combinatorics.
Area of Science:
- Dynamical Systems and Chaos Theory
- Statistical Physics
- Combinatorics
Background:
- Coupled circle maps are fundamental models for studying complex dynamics.
- Repulsive (inhibitory) coupling introduces unique behaviors not seen in attractive coupling.
- Characterizing different dynamical states like synchrony, traveling waves, and chaos is crucial.
Purpose of the Study:
- To investigate the utility of persistence as a measure for characterizing dynamical states in coupled circle maps with repulsive coupling.
- To analyze the scaling behavior of persistence in the traveling wave state.
- To develop a theoretical explanation for the observed persistence scaling.
Main Methods:
- Analysis of persistence in coupled circle maps with repulsive coupling.
- Investigation of power-law scaling in the traveling wave regime.
- Development of a cellular automata model.
- Application of combinatorial theory, specifically Motzkin numbers.
Main Results:
- Persistence effectively distinguishes between synchronous, traveling wave, and spatiotemporally chaotic states.
- In the traveling wave state, persistence exhibits power-law decay.
- This power-law scaling is observed across the entire dynamical phase, not just at transition points, with a consistent exponent.
- A cellular automata model successfully replicates the qualitative features of the traveling wave regime.
Conclusions:
- Persistence is a robust tool for characterizing complex dynamics in coupled systems.
- The observed power-law decay in traveling waves provides new insights into dynamical system transitions.
- Combinatorial arguments involving Motzkin numbers offer a theoretical basis for the scaling behavior.
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