Volume 102, Number 2, April 2013
|Number of page(s)||6|
|Published online||06 May 2013|
Oscillation suppression and synchronization: Frequencies determine the role of control with time delays
1 School of Mathematical Sciences and Centre for Computational Systems Biology, Fudan University Shanghai 200433, China
2 Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), Ministry of Education - China
3 Potsdam Institute for Climate Impact Research - D-14412 Potsdam, Germany
4 Department of Physics, Humboldt University of Berlin - D-12489 Berlin, Germany
Received: 25 January 2013
Accepted: 2 April 2013
In this letter, we find how the frequency of an oscillation determines the exact form of the control for suppressing the oscillation through feedback controls with time delays. These results are based on necessary and sufficient conditions we analytically established for the stability of a dynamical system with feedback control and time delays. We also interpret how these conditions change as the time delay either is equal to zero or becomes larger appropriately. All the analytical and numerical results are illustrated by suppressing the oscillations of the FitzHugh-Nagumo model and by the oscillation death and synchronization phenomena observed in a complex dynamical network with time-delayed couplings. Our findings could be potentially useful for modulating oscillations through proper control devices in various fields.
PACS: 05.45.Xt – Synchronization; coupled oscillators / 02.30.Ks – Delay and functional equations / 89.75.-k – Complex systems
© EPLA, 2013
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