Kestutis Pyragas

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Delayed feedback control of chaos is well known as an effective method for stabilizing unstable periodic orbits embedded in chaotic attractors. However, it had been shown that the method works only for a certain class of periodic orbits characterized by a finite torsion. Modification based on an unstable delayed feedback controller is proposed in order to(More)
Time-delayed feedback control is well known as a practical method for stabilizing unstable periodic orbits embedded in chaotic attractors. The method is based on applying feedback perturbation proportional to the deviation of the current state of the system from its state one period in the past, so that the control signal vanishes when the stabilization of(More)
An adaptive dynamic state feedback controller for stabilizing and tracking unknown steady states of dynamical systems is proposed. We prove that the steady state can never be stabilized if the system and controller in sum have an odd number of real positive eigenvalues. For two-dimensional systems, this topological limitation states that only an unstable(More)
A simple adaptive controller based on a low-pass filter to stabilize unstable steady states of dynamical systems is considered. The controller is reference-free; it does not require knowledge of the location of the fixed point in the phase space. A topological limitation similar to that of the delayed feedback controller is discussed. We show that the(More)
We propose an algorithm of coupling design for a long-term anticipating synchronization of chaos and demonstrate its efficacy for typical chaotic systems: namely, the Rössler system, the double-scroll Chua circuit, and the Lorenz system. The maximum prediction time attained with our algorithm is several times larger than with the diagonal coupling usually(More)
We develop an analytical approach for the delayed feedback control of the Lorenz system close to a subcritical Hopf bifurcation. The periodic orbits arising at this bifurcation have no torsion and cannot be stabilized by a conventional delayed feedback control technique. We utilize a modification based on an unstable delayed feedback controller. The(More)
The delayed feedback control (DFC) methods are noninvasive, which means that the control signal vanishes if the delay time is adjusted to be equal to the period of a target unstable periodic orbit (UPO). If the delay time differs slightly from the UPO period, a nonvanishing periodic control signal is observed. We derive an analytical expression for this(More)
A modified delayed feedback control algorithm with the improved global properties is proposed. The modification is based on the ergodic features of chaotic systems. We do not perturb the system until its state approaches a desired unstable periodic orbit and then we activate the delayed feedback control force. To evaluate the closeness of the system state(More)
We investigate the effect of a homogeneous high-frequency stimulation (HFS) on a one-dimensional chain of coupled excitable elements governed by the FitzHugh-Nagumo equations. We eliminate the high-frequency term by the method of averaging and show that the averaged dynamics depends on the parameter A=a/ω equal to the ratio of the amplitude a to the(More)
The act-and-wait control algorithm is proposed to suppress synchrony in globally coupled oscillatory networks in the situation when the simultaneous registration and stimulation of the system is not possible. The algorithm involves the periodic repetition of the registration (wait) and stimulation (act) stages, such that in the first stage the mean field of(More)