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Delayed feedback control of unstable steady states with high-frequency modulation of the delay
(2013-09)
;
Jüngling, Thomas
;
Urumov, Viktor
;
Schöll, Eckehard
We analyze the stabilization of unstable steady states by delayed feedback control with a periodic time-varying delay in the regime of a high-frequency modulation of the delay. The average effect of the delayed feedback term in the control force is equivalent to a distributed delay in the interval of the modulation, and the obtained distribution depends on the type of the modulation. In our analysis we use a simple generic normal form of an unstable focus, and investigate the effects of phase-dependent coupling and the influence of the control loop latency on the controllability. In addition, we have explored the influence of the modulation of the delays in multiple delay feedback schemes consisting of two independent delay lines of Pyragas type. A main advantage of the variable delay is the considerably larger domain of stabilization in parameter space.
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Control of amplitude chimeras by time delay in oscillator networks
(2017-04)
Gjurchinovski, Aleksandar
;
Schöll, Eckehard
;
Zakharova, Anna
We investigate the influence of time-delayed coupling in a ring network of nonlocally coupled Stuart-Landau oscillators upon chimera states, i.e., space-time patterns with coexisting partially coherent and partially incoherent domains. We focus on amplitude chimeras, which exhibit incoherent behavior with respect to the amplitude rather than the phase and are transient patterns, and we show that their lifetime can be significantly enhanced by coupling delay. To characterize their transition to phase-lag synchronization (coherent traveling waves) and other coherent structures, we generalize the Kuramoto order parameter. Contrasting the results for instantaneous coupling with those for constant coupling delay, for time-varying delay, and for distributed-delay coupling, we demonstrate that the lifetime of amplitude chimera states and related partially incoherent states can be controlled, i.e., deliberately reduced or increased, depending upon the type of coupling delay.
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Amplitude death and chimera patterns in complex networks with time delays
(Russian Academy of Sciences, Institute of Applied Physics, Nizhny Novgorod, 2017)
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Schöll, Eckehard
;
Zakharova, Anna
We study the conditions of amplitude death in a network of delay-coupled limit cycle oscillators with time-varying delay coupling. By generalizing the master stability function formalism, we analyze the amplitude death regimes in a ring and a multiplex network of Stuart-Landau oscillators. We further investigate the influence of time delay (constant, time-varying, or distributed) on the dynamical regimes and the lifetime of amplitude chimera states in the case when coupling breaks the rotational S1 symmetry. We demonstrate that the lifetime of amplitude chimeras and related incoherent states can be deliberately reduced or increased, depending upon the type of coupling delay.
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Control of amplitude chimeras by time delay in dynamical networks
(The European Nonlinear Dynamics Conference (ENOC), Congressline Ltd., Budapest, 2017)
Schöll, Eckehard
;
Zakharova, Anna
;
We investigate the influence of time-delayed coupling in a ring network of non-locally coupled Stuart-Landau oscillators upon chimera states, i.e., space-time patterns with coexisting partially coherent and partially incoherent domains. We focus on amplitude chimeras which exhibit incoherent behavior with respect to the amplitude rather than the phase and are transient patterns, and show that their lifetime can be significantly enhanced by coupling delay. To characterize their transition to phase-lag synchronization (coherent traveling waves) and other coherent structures, we generalize the Kuramoto order parameter. Contrasting the results for instantaneous coupling with those for constant and for time-varying coupling delays, we demonstrate that the lifetime of amplitude chimera states and related partially incoherent states can be controlled, i.e., deliberately reduced or increased, depending upon the type of coupling delay.
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Amplitude death in oscillator networks with variable-delay coupling
(American Physical Society (APS), 2014-03-24)
Gjurchinovski, Aleksandar
;
Zakharova, Anna
;
Schöll, Eckehard

Faculty of Natural Sciences and Mathematics

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