Controlling cluster synchronization by adapting the topology
Judith Lehnert1, Philipp Hövel2, Anton Selivanov3
1Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 7, 2014
Summary
This study introduces an adaptive control scheme for synchronizing delay-coupled networks. The method dynamically adjusts network topology to achieve desired synchronization states, robustly controlling complex systems.
Area of Science:
- Complex Systems and Network Science
- Nonlinear Dynamics and Control Theory
Background:
- Synchronization phenomena are crucial in various natural and engineered systems.
- Controlling synchronization in networks with time delays presents significant challenges.
Purpose of the Study:
- To develop an adaptive control scheme for achieving in-phase and cluster synchronization in delay-coupled networks.
- To ensure the control scheme is robust against varying initial conditions and coupling parameters.
Main Methods:
- Utilized the speed-gradient method to adapt network topology dynamically.
- Investigated the role of excitatory and inhibitory links in stabilizing cluster states.
- Analyzed the impact of delay time as a critical parameter.
Main Results:
- Successfully demonstrated robust control of synchronization in delay-coupled networks.
- Identified a specific interplay of link types and delay time for stabilizing desired cluster states.
- Showcased the ability to construct networks exhibiting specific cluster states and oscillation frequencies.
Conclusions:
- The proposed adaptive control scheme effectively manages synchronization in complex networks.
- The method's robustness and applicability to generic models like the Stuart-Landau oscillators suggest broad potential.
- Potential applications span physics, chemistry, technology, and life sciences, highlighting the universality of the findings.
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