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- Kestutis Pyragas
- Philosophical transactions. Series A…
- 2006

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)

- K Pyragas
- Physical review letters
- 2001

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)

- K Pyragas, V Pyragas, I Z Kiss, J L Hudson
- Physical review. E, Statistical, nonlinear, and…
- 2004

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, V Pyragas, I Z Kiss, J L Hudson
- Physical review letters
- 2002

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)

- K Pyragas
- Physical review. E, Statistical, nonlinear, and…
- 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)

- Kestutis Pyragas, Viktoras Pyragas
- Physical review. E, Statistical, nonlinear, and…
- 2009

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)

- Kestutis Pyragas, Tatjana Pyragiene
- Physical review. E, Statistical, nonlinear, and…
- 2008

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)

- K. PYRAGAS
- 1998

Secure communication via chaotic synchronization is demonstrated using dynamical systems governed by delay deferential equations. Strange attractors of such systems can have an arbitrarily large number of positive Lyapunov exponents giving rise to very complex time signals. This feature can provide high security of masked messages.

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)

- K. Pyragas
- 2003

Time delayed-feedback control is an efficient method for stabilizing unstable periodic orbits of chaotic systems. The method is based on applying feedback 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 the desired orbit is attained. A brief… (More)