Kestutis Pyragas

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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)
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)
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)
  • K Pyragas
  • 2002
Time-delayed feedback control is an efficient method for stabilizing unstable periodic orbits of chaotic systems. If the equations governing the system dynamics are known, the success of the method can be predicted by a linear stability analysis of the desired orbit. Unfortunately, the usual procedures for evaluating the Floquet exponents of such systems(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 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 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)
A novel, very simple chaotic oscillator is described. It is intended for training laboratories accompanying courses on nonlinear dynamics and chaos for undergraduate, postgraduate and PhD students. The oscillator consists of an operational amplifier, an LCR resonance loop, an extra capacitor, a diode as a nonlinear element and three auxiliary resistors.(More)