Small-world networks exhibit pronounced intermittent synchronization
Anshul Choudhary1, Chiranjit Mitra2, Vivek Kohar3
1Theoretical Physics/Complex Systems, ICBM, Carl von Ossietzky University of Oldenburg, 26111 Oldenburg, Germany.
Chaos (Woodbury, N.Y.)
|December 3, 2017
Summary
We discovered intermittent synchronization in chaotic Rössler oscillator networks. Network structure, not just largest Lyapunov exponent, predicts this complex dynamic behavior, challenging existing models.
Area of Science:
- Complex systems
- Network science
- Nonlinear dynamics
Background:
- Watts-Strogatz networks exhibit small-world properties, bridging regular and random networks.
- Master Stability Function (MSF) is a common method for analyzing synchronization stability in coupled oscillators.
- Previous studies often focus on the largest Lyapunov exponent for synchronization prediction.
Purpose of the Study:
- To investigate temporally intermittent synchronization in Watts-Strogatz networks of chaotic Rössler oscillators.
- To explore the role of Lyapunov spectra beyond the largest exponent in predicting synchronization dynamics.
- To analyze the global stability and characteristics of intermittent synchronization across varying network rewiring probabilities.
Main Methods:
- Simulations of coupled chaotic Rössler oscillators on Watts-Strogatz networks.
- Application of Master Stability Function (MSF) analysis.
- Analysis of the full Lyapunov spectra transversal to the synchronization manifold.
- Estimation of global stability using the fraction of state-space volume.
Main Results:
- Observed phenomenon of temporally intermittent synchronization and desynchronization.
- Identified the difference in Lyapunov spectra as a crucial indicator for intermittent synchronization, beyond MSF predictions.
- Found a surprisingly large fraction of state-space volume for intermittent synchronization in the small-world regime.
- Characterized the nature and dominance of intermittency with varying network rewiring probability.
Conclusions:
- The full Lyapunov spectra are essential for understanding intermittent synchronization in complex networks.
- Intermittent synchronization can be prevalent even in network regimes previously considered optimal for stable synchronization.
- Network rewiring probability significantly influences the dynamics and stability of synchronized states.
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