Kestutis Pyragas

Learn 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)
Using Hodgkin–Huxley and isolated subthalamic nucleus (STN) model neurons as examples, we show that electrical high-frequency stimulation (HFS) suppresses sustained neuronal spiking. The mechanism of suppression is explained on the basis of averaged equations derived from the original neuron equations in the limit of high frequencies. We show that for(More)
We demonstrate theoretically and experimentally that the unstable delayed feedback controller is an efficient tool for stabilizing torsion-free unstable periodic orbits in nonautonomous chaotic systems. To improve the global control performance we introduce a two-step control algorithm. The problem of a linear stability of the system under delayed feedback(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)
We consider a weakly nonlinear van der Pol oscillator subjected to a periodic force and delayed feedback control. Without control, the oscillator can be synchronized by the periodic force only in a certain domain of parameters. However, outside of this domain the system possesses unstable periodic orbits that can be stabilized by delayed feedback(More)
We consider the delayed feedback control of a torsion-free unstable periodic orbit originated in a dynamical system at a subcritical Hopf bifurcation. Close to the bifurcation point the problem is treated analytically using the method of averaging. We discuss the necessity of employing an unstable degree of freedom in the feedback loop as well as a(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)