The effect of coherence resonance can change the firing process in noise-driven excitable systems towards rather regular dynamics. For such stochastic oscillators, we study the synchronization in terms of locking of the peak frequencies in the power spectrum and also in terms of phase locking. Our investigations are based on numerical simulations of coupled Morris-Lecar neuron models and on fullscale experiments with coupled monovibrator electronic circuits. PACS numbers: 05.45.Xt, 05.40.Ca, 84.30.Ng, 87.17.Nn During the last few decades, the interest in nonlinear science has greatly exploded as new types of oscillatory behavior, namely, chaotic and stochastic ones, have exploded. The collective behavior of systems composed of these interacting functional units can be regulated by a cooperative property, like synchronization phenomena.For regular oscillations, when phase locking takes place, a stabilization of the phase shift between the interacting modes occurs, and the natural frequencies of oscillations become equal [1]. The classical results for regular oscillations have been generalized to some classes of chaotic oscillations. It has been shown that the synchronization in systems demonstrating the period-doubling route to chaos can be described in terms of fundamental frequency locking [2]. Following [3], synchronization of chaotic systems can be generalized to the phase synchronization.Synchronization phenomena have also been investigated in nonlinear stochastic systems. Locking of the mean switching frequency and some kind of phase locking have been discovered both in periodically forced and in coupled noise-driven bistable systems [4,5]. Even for noisy signals, the phase description was found to be useful for the analysis of synchronization in human cardio-respiratory systems [6], for instance. These investigations are based on the classical approach to synchronization in the presence of noise [7]. The phase locking for stochastic systems is considered as an event lasting for a finite time and is described with the diffusion of phase [5] or by the shape of the phase difference distribution function [6].Recently, a phenomenon called autonomous stochastic resonance [8] or coherence resonance (CR) [9,10] has been observed in excitable systems perturbed by noise and without external periodic forcing. Note that, in this case, a deterministic system does not exhibit any selfsustained oscillations but noise of an optimal intensity generates a quasiregular signal. Pikovsky and Kurths [9] explained the effect of CR by different noise dependences of the activation and the excursion times. Most recently, the CR effect has been confirmed by means of electronic experiments [11]. Figure 1 displays the typical shape of the power spectra in a regime of CR obtained for the relaxation-type MorrisLecar (ML) neuron model [12] driven by the noise. Each spectrum possesses a well-defined global maximum which might be associated with the natural frequency of oscillations. The regularized behavior is observed within a reasonab...

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Summary:Purpose: Application of independent component analysis (ICA) to interictal EEGs and to event-related potentials has helped noise reduction and source localization. However, ICA has not been used for the analysis of ictal EEGs in partial seizures. In this study, we applied ICA to the ictal EEGs of patients with medial temporal lobe epilepsy (TLE) and investigated whether ictal components can be separated and whether they indicate correct lateralization.Methods: Twenty-four EEGs from medial TLE patients were analyzed with the extended ICA algorithm. Among the resultant 20 components in each EEG, we selected components with an ictal nature and reviewed their corresponding topographic maps for the lateralization. We then applied quantitative methods for the verification of increased quality of the reconstructed EEGs.Results: All ictal EEGs were successfully decomposed into one or more ictal components and nonictal components. After EEG reconstruction with exclusion of artifacts, the lateralizing power of the ictal EEG was increased from 75 to 96%.Conclusions: ICA can separate successfully the manifold components of ictal rhythms and can improve EEG quality. Key Words: Independent component analysis-Ictal component-Ictal EEG-Medial temporal lobe epilepsyArtifact.EEG recording is an essential step to localize irritative and ictal-onset zones, especially when epilepsy surgery is being considered. To localize the ictal-onset zone, a well-trained epileptologist visually inspects the EEG recordings. Identification of an unambiguous ictal-onset zone is often difficult because of unwanted artifacts arising from muscle contraction or eye movements. Recently a new data-processing technique, independent component analysis (ICA), was developed for the purpose of resolving multiple mixtures of data into statistically independent components (1,2). If we apply this method of analysis to EEG data, the EEG can be decomposed into spatiotemporal components that have fixed potential field distributions and maximally independent waveforms. The method has been found to be quite successful in separating artifacts or noisy components from the multichannel interictal EEG (3), recordings of event-related potentials (4), and functional magnetic resonance imaging (MRI) (5).We applied ICA to multichannel ictal EEG recordings in medial temporal lobe epilepsy (TLE). The ICA transforms the multichannel EEG data into an equal number of spatial patterns and their associated temporal waveforms, which are statistically independent of each other. The purpose of this study was to provide answers for the following two questions: Can ICA separate successfully ictal rhythms from noisy ictal EEGs of partial seizures? Can ICA help to lateralize medial TLE? MATERIALS AND METHODSWe applied ICA to 11 ictal EEGs from seven right medial TLE patients and to 13 EEGs from seven left medial TLE patients. All patients had been seizure free for more than a year after standard anterior temporal lobectomy with amygdalohippocampectomy. The diagnosis of each patien...

The effect of coherence resonance can change the firing process in noise-driven excitable systems towards rather regular dynamics. This effect provides a mechanism of the generation of stochastic oscillations whose characteristics are controlled by noise intensity. Following this, a noisy excitable system can be considered as a corehence resonance oscillator. For such functional units, we investigate the mutual and forced synchronization in terms of locking of the peak frequencies in the power spectrum and also in terms of phase locking. The connection of synchronization phenomenon of noise-induced oscillations and coherence resonance effect is discussed. The examples, studied numerically and experimentally, include Morris-Lecar neuron model and a monovibrator electronic circuit, respectively.

Recently it was shown that dephasing of diffusively coupled neural oscillators leads to a new class of bursting phenomena, where neural oscillators switch between high and low oscillation amplitudes. To analyze this behavior we study a system of three-coupled neurons, which is the most simple one that shows chaotic bursting behavior. For the intermediate values of coupling constant kc, the chaotic bursting behavior occurs. For a quantitative analysis of chaotic bursting, we introduce three mean activities of oscillators. From the Poincaré sections we find a period-doubling route to chaos. We illustrate the busting behavior in terms of competition of the single oscillator behavior with the collective one arising from the diffusive coupling of oscillators.

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