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Dynamics, correlation scaling, and synchronization behavior in rings of delay-coupled oscillators
Guy Van der Sande1, Miguel C Soriano, Ingo Fischer
1Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain. guy.van.der.sande@vub.ac.be
Summary
We reveal simple scaling in the dynamics of delay-coupled nonlinear oscillators. Ring correlations can be predicted from single systems, enabling synchronization in coupled oscillator networks.
Area of Science:
- Nonlinear dynamics
- Complex systems
- Network science
Background:
- Unidirectional coupling and propagation delays are crucial in many natural and engineered systems.
- Understanding emergent dynamics in coupled oscillator networks is a fundamental challenge.
Purpose of the Study:
- To investigate the dynamics of unidirectionally delay-coupled nonlinear oscillators arranged in a ring.
- To explore the relationship between correlation properties in ring networks and single delayed feedback systems.
- To demonstrate synchronization phenomena in coupled oscillator chains and rings.
Main Methods:
- Cascading unidirectionally coupled nonlinear oscillators in a ring configuration with fixed total propagation delay.
- Analyzing correlation properties and autocorrelation functions.
- Coupling ring elements to external chains of identical oscillators.
Main Results:
- Demonstrated simple scaling behavior of correlation properties in the ring network.
- Showed that ring correlations can be deduced from the autocorrelation of a single delayed feedback system.
- Achieved complete synchronization between ring and chain elements.
- Observed generalized synchronization in other elements, even when initially uncorrelated.
Conclusions:
- The study reveals predictable scaling laws for correlation properties in delay-coupled oscillator rings.
- A single delayed feedback system's autocorrelation can characterize the entire ring's dynamics.
- Synchronization phenomena, including complete and generalized synchronization, can be effectively achieved and demonstrated in these complex networks.
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