Interacting Coherence Resonance Oscillators

Abstract

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...

Regular Wave Propagation Out of Noise in Chemical Active Media

“…With this unified perspective we highlight the specificities of these phenomenologies in relation to other celebrated noise-constructive effects, typical of either forced or autonomous extended systems, i.e., array enhanced stochastic resonance [11,12], taming spatiotemporal chaos with disorder [13], noise-enhanced signal propagation [14,15], and noise-induced synchronization to global oscillations for arrays of excitable units [16,17] or coherence resonance oscillators [18,19]. Experiments were carried out using thin (0.3 mm), squared (3 3 3 cm 2 ) film of silica gel, in which the light-sensitive catalyst, ruthenium-bipyridyl [Ru(bpy)], was immobilized [9] [solution of 15% sodium silicate, 1.5 mM Ru͑bpy͒ 21 3 and 1M H 2 SO 4 ] prepared as in Ref.…”

Spatiotemporal order out of noise

“…The most closely related are those by Han et al ͑1999͒, using monovibrator electronic circuits, who reported a small-͑spatial͒ scale realization of stochastic coherence with a pair of identical "stochastic" oscillators. With similar equipment, the same authors detected more recently noise-induced multimode FIG.…”

Regularization of chaos by noise in electrically driven nanowire systems

“…Theoretical [36][37][38][39][40][41][42] and experimental [43][44][45] works on coherence resonance addressed excitable dynamical systems that typically generate bursting time series. In such a system, there is usually a reference or a "silent" state, e.g., a fixed point, near which a trajectory can spend long stretches of time.…”

“…Quantitatively, associated with coherence resonance, the temporal regularity of the system dynamics depends on the noise amplitude and it can be maximized by noise of optimal amplitude. There were extensive studies of coherence resonance in the past decades both theoretically [36][37][38][39][40][41][42] and experimentally [43][44][45]. For low-dimensional chaotic systems, coherence resonance has also been studied [33,34,[46][47][48].…”