The universal mechanism resulting in the generalized synchronization regime arising in the chaotic oscillators with the dissipative coupling has been described. The reasons for the generalized synchronization occurrence may be clarified by means of a modified system approach. The main results are illustrated by unidirectionally coupled Rössler systems, Rössler and Lorenz systems, and logistic maps.

This paper deals with the chaotic oscillator synchronization. An approach to the synchronization of chaotic oscillators has been proposed. This approach is based on the analysis of different time scales in the time series generated by the coupled chaotic oscillators. It has been shown that complete synchronization, phase synchronization, lag synchronization, and generalized synchronization are the particular cases of the synchronized behavior called "time-scale synchronization." The quantitative measure of chaotic oscillator synchronous behavior has been proposed. This approach has been applied for the coupled Rössler systems and two coupled Chua's circuits.

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We show that resonant electron transport in semiconductor superlattices with an applied electric and tilted magnetic field can, surprisingly, become more pronounced as the lattice and conduction electron temperature increases from 4.2 K to room temperature and beyond. It has previously been demonstrated that at certain critical field parameters, the semiclassical trajectories of electrons in the lowest miniband of the superlattice change abruptly from fully localised to completely unbounded. The unbounded electron orbits propagate through intricate web patterns, known as stochastic webs, in phase space, which act as conduction channels for the electrons and produce a series of resonant peaks in the electron drift velocity versus electric field curves. Here, we show that increasing the lattice temperature strengthens these resonant peaks due to a subtle interplay between thermal population of the conduction channels and transport along them. This enhances both the electron drift velocity and the influence of the stochastic webs on the current-voltage characteristics, which we calculate by making self-consistent solutions of the coupled electron transport and Poisson equations throughout the superlattice. These solutions reveal that increasing the temperature also transforms the collective electron dynamics by changing both the threshold voltage required for the onset of self-sustained current oscillations, produced by propagating charge domains, and the oscillation frequency.

The ultimate goal of epileptology is the complete abolishment of epileptic seizures. This might be achieved by a system that predicts seizure onset combined with a system that interferes with the process that leads to the onset of a seizure. Seizure prediction remains, as of yet, unresolved in absence-epilepsy, due to the sudden onset of seizures. We have developed a real-time absence seizure prediction algorithm, evaluated it and implemented it in an on-line, closed-loop brain stimulation system designed to prevent the spike-wave-discharges (SWDs), typical for absence epilepsy, in a genetic rat model. The algorithm corretly predicted 88% of the SWDs while the remaining were quickly detected. A high number of false-positive detections occurred mainly during light slow-wave-sleep. Inclusion of criteria to prevent false-positives greatly reduced the false alarm rate but decreased the sensitivity of the algoritm. Implementation of the latter version into a closed-loop brain-stimulation-system resulted in a 72% decrease in seizure activity. In contrast to long standing beliefs that SWDs are unpredictable, these results demonstrate that they can be predicted and that the development of closed-loop seizure prediction and prevention systems is a feasable step towards interventions to attain control and freedom from epileptic seizures.

We study excitation and suppression of chimera states in an ensemble of nonlocally coupled oscillators arranged in a framework of multiplex network. We consider the homogeneous network (all identical oscillators) with different parametric cases and interlayer heterogeneity by introducing parameter mismatch between the layers. We show the feasibility to suppress chimera states in the multiplex network via moderate interlayer interaction between a layer exhibiting chimera state and other layers which are in a coherent or incoherent state. On the contrary, for larger interlayer coupling, we observe the emergence of identical chimera states in both layers which we call an interlayer chimera state. We map the spatiotemporal behavior in a wide range of parameters, varying interlayer coupling strength and phase lag in two and three multiplexing layers. We also prove the emergence of interlayer chimera states in a multiplex network via evaluation of a continuous model. Furthermore, we consider the two-layered network of Hindmarsh-Rose neurons and reveal that in such a system multiplex interaction between layers is capable of exciting not only the synchronous interlayer chimera state but also nonidentical chimera patterns.

This paper presents the result of the investigation of chaotic oscillator synchronization. A new approach for detecting of synchronized behaviour of chaotic oscillators has been proposed. This approach is based on the analysis of different time scales in the time series generated by the coupled chaotic oscillators. This approach has been applied for the coupled Rössler and Lorenz systems.

Abstract. -A new behavior type of unidirectionally coupled chaotic oscillators near the generalized synchronization transition has been detected. It has been shown that the generalized synchronization appearance is preceded by the intermitted behavior: close to threshold parameter value the coupled chaotic systems demonstrate the generalized synchronization most of the time, but there are time intervals during which the synchronized oscillations are interrupted by non-synchronous bursts. This type of the system behavior has been called intermitted generalized synchronization (IGS) by analogy with intermitted lag synchronization (ILS) [Phys. Rev. E 62, 7497 (2000)].Synchronization [1,2] of interacting chaotic oscillators is one of the fundamental phenomena of nonlinear dynamics. Recently several types of chaotic synchronization have been observed in coupled nonlinear oscillators. These are phase synchronization (PS) [3][4][5], lag synchronization (LS) [6][7][8], complete synchronization (CS) [9][10][11][12] and generalized synchronization (GS) [13][14][15]. It is important to note that GS may also takes place in the non-oscillatory chaotic systems (see [16] for detail). All synchronization types are interrelated (see for detail [7,13,17]), but the relationship between them is not completely clarified yet. In recent works [18][19][20][21] it has been shown that all these synchronization types may be considered from the common point of view as different manifestations of one universal phenomenon.It has also been found that onsets of phase and lag synchronization types are preceded by intermittent behavior. Close to the threshold parameter value the coupled chaotic systems demonstrate synchronized dynamics most of the time, but there are time intervals during which the synchronized oscillations are interrupted by non-synchronous behavior. These pretransitional intermittencies have been described in [6,22,23] for the case of lag synchronization and in [24][25][26] for phase synchronization, respectively.Due to the existence of unifying framework of coupled chaotic oscillators synchronization one can also expect the intermitted behavior at the threshold of the generalized synchronization appearance. In this work we consider the behavior of coupled chaotic oscillators close to the coupling parameter value corresponding to the onset of generalized synchronization regime. As it will be shown below the generalized synchronization appearance is also preceded by the intermitted behavior in the same way as the phase synchronization and lag c EDP Sciences