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)
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 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)
A mathematical model of a recently suggested chaos oscillator for educational purposes is treated and numerical results are presented. Bifurcation diagrams, phase portraits, power spectra, Lya-punov exponents are simulated. In addition, the Feigenbaum number is estimated.
Frequency-domain analysis of the recently suggested analogue signal predictor is performed. In addition, the operation of the circuit is demonstrated in the high frequency and very high frequency ranges by means of PSPICE simulator employing high-speed operational amplifiers.