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Properties of zero-lag long-range synchronization via dynamical relaying.
1International Center for Complex Systems, Universidade Federal do Rio Grande do Norte, Natal, Rio Grande do Norte CEP 59078-970, Brazil. mariav_us@yahoo.com
Chaos (Woodbury, N.Y.)
|April 8, 2010
Summary
A third element can enable zero-lag synchronization between two systems, even with delays. This study explores this phenomenon in Rössler and Kuramoto oscillators and logistic maps.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Network science
Background:
- Fischer et al. (2006) introduced zero-lag long-range isochronous synchronization via dynamical relaying.
- This phenomenon allows synchronization between two systems (A and C) when a third system (B) is introduced between them, overcoming parameter space limitations.
Purpose of the Study:
- To investigate the mechanisms of zero-lag long-range synchronization using a dynamical relay system.
- To analyze the phenomenon in different types of coupled oscillators and maps.
Main Methods:
- Studied coupled Rössler oscillators to identify synchronization modes (antiphase, in-phase, anticipating).
- Analyzed coupled Kuramoto oscillators for periodic orbits, enabling analytical calculations.
- Investigated coupled logistic maps to determine conditions for synchronization.
Main Results:
- Zero-lag synchronization in Rössler oscillators occurs via antiphase, in-phase, or anticipating synchronization depending on feedback and delay.
- Similar synchronization phenomena were observed in Kuramoto oscillators.
- For logistic maps, synchronization is possible in regions with a negative transversal Lyapunov exponent.
Conclusions:
- Dynamical relaying provides multiple pathways for achieving zero-lag synchronization in complex systems.
- The study confirms and extends the understanding of relay-induced synchronization across different dynamical systems.
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