Time-delayed feedback control of coherence resonance near subcritical Hopf bifurcation: theory versus experiment

Using the model of a generalized Van der Pol oscillator in the regime of subcritical Hopf bifurcation we investigate the influence of time delay on noise-induced oscillations. It is shown that for appropriate choices of time delay either suppression or enhancement of coherence resonance can de achieved. Analytical calculations are combined with numerical simulations and experiments on an electronic circuit

Two Scenarios of Breaking Chaotic Phase Synchronization

Two types of phase synchronization (accordingly, two scenarios of breaking phase synchronization) between coupled stochastic oscillators are shown to exist depending on the discrepancy between the control parameters of interacting oscillators, as in the case of classical synchronization of periodic oscillators. If interacting stochastic oscillators are weakly detuned, the phase coherency of the attractors persists when phase synchronization breaks. Conversely, if the control parameters differ considerably, the chaotic attractor becomes phase-incoherent under the conditions of phase synchronization break.Comment: 8 pages, 7 figure

Modeling Brain Resonance Phenomena Using a Neural Mass Model

Stimulation with rhythmic light flicker (photic driving) plays an important role in the diagnosis of schizophrenia, mood disorder, migraine, and epilepsy. In particular, the adjustment of spontaneous brain rhythms to the stimulus frequency (entrainment) is used to assess the functional flexibility of the brain. We aim to gain deeper understanding of the mechanisms underlying this technique and to predict the effects of stimulus frequency and intensity. For this purpose, a modified Jansen and Rit neural mass model (NMM) of a cortical circuit is used. This mean field model has been designed to strike a balance between mathematical simplicity and biological plausibility. We reproduced the entrainment phenomenon observed in EEG during a photic driving experiment. More generally, we demonstrate that such a single area model can already yield very complex dynamics, including chaos, for biologically plausible parameter ranges. We chart the entire parameter space by means of characteristic Lyapunov spectra and Kaplan-Yorke dimension as well as time series and power spectra. Rhythmic and chaotic brain states were found virtually next to each other, such that small parameter changes can give rise to switching from one to another. Strikingly, this characteristic pattern of unpredictability generated by the model was matched to the experimental data with reasonable accuracy. These findings confirm that the NMM is a useful model of brain dynamics during photic driving. In this context, it can be used to study the mechanisms of, for example, perception and epileptic seizure generation. In particular, it enabled us to make predictions regarding the stimulus amplitude in further experiments for improving the entrainment effect

Phase dynamics of two coupled oscillators under external periodic force

The effect of synchronization has been studied in a system of two coupled Van der Pol oscillators under external harmonic force. The analysis has been carried out using the phase approach. The mechanisms of complete and partial synchronization have been established. The main type of bifurcation described in this paper is the saddle-node bifurcation of invariant curves that corresponds to the saddle-node bifurcation of two-dimensional tori in the complete system of differential equations for the dynamical system under study

Stochastic self-sustained oscillations of non-autonomous systems

In the present minireview, we analyze autonomous and non-autonomous oscillations of dynamical and stochastic systems in the framework of common concepts. We introduce the definition of an attractor for a non-autonomous system. We also propose the definition of self-sustained oscillations, which can be applied for both autonomous and non-autonomous systems. We consider noise-induced oscillations and formulate the definition of stochastic self-sustained oscillations for this case. All the statements made in this work are illustrated by particular examples

Phase multistability of synchronous chaotic oscillations

The paper describes the sequence of bifurcations leading to multistability of periodic and chaotic synchronous attractors for the coupled Rössler systems which individually demonstrate the Feigenbaum route to chaos. We investigate how a frequency mismatch affects this phenomenon. The role of a set of coexisting synchronous regimes in the transitions to and between different forms of synchronization is studied

Numerical and experimental studies of attractors in memristor-based Chua's oscillator with a line of equilibria. Noise-induced effects

The intrinsic features of systems with a line of equilibria are analyzed by studying of memristor-based Chua's oscillator. The analog modeling of the system is carried out together with its numerical simulation. The characteristics of stochastic oscillations in the system under study are explored in the presence of noise. The issues concerning the physical realization of a system with a line of equilibria are also considered