This paper is devoted to the problem of synchronization of dynamical systems in chaotic oscillations regimes. The authors attempt to use the ideas of synchronization and its mechanisms on a certain class of chaotic oscillations. These are chaotic oscillations for which one can pick out basic frequencies in their power spectra. The physical and computer experiments were carried out for the system of two coupled auto-oscillators. The experimental installation permitted one to realize both unidirectional coupling (external synchronization) and symmetrical coupling (mutual synchronization). An auto-oscillator with an inertial nonlinearity was chosen as a partial subsystem. It possesses a chaotic attractor of spiral type in its phase space. It is known that such chaotic oscillations have a distinguished peak in the power spectrum at the frequency f0 (basic frequency). In the experiments, one could make the basic frequencies of partial oscillators equal or different. The bifurcation diagrams on the plane of control parameters "detuning" and "coupling" were constructed and analyzed. The results of investigations permit one to conclude that classical ideas of synchronization can be applied to chaotic systems of the mentioned type. Two mechanisms of chaos synchronization were established: 1) basic frequency locking and 2) basic frequency suppression. The bifurcational background of these mechanisms was created using numerical analysis on a computer. This allowed one to analyze the evolution of different oscillation characteristics under the influence of synchronization.

No 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...

No abstract

No abstract

Through regulation of the extracellular fluid volume, the kidneys provide important long-term regulation of blood pressure. At the level of the individual functional unit (the nephron), pressure and flow control involves two different mechanisms that both produce oscillations. The nephrons are arranged in a complex branching structure that delivers blood to each nephron and, at the same time, provides a basis for an interaction between adjacent nephrons. The functional consequences of this interaction are not understood, and at present it is not possible to address this question experimentally. We provide experimental data and a new modeling approach to clarify this problem. To resolve details of microvascular structure, we collected 3D data from more than 150 afferent arterioles in an optically cleared rat kidney. Using these results together with published micro-computed tomography (μCT) data we develop an algorithm for generating the renal arterial network. We then introduce a mathematical model describing blood flow dynamics and nephron to nephron interaction in the network. The model includes an implementation of electrical signal propagation along a vascular wall. Simulation results show that the renal arterial architecture plays an important role in maintaining adequate pressure levels and the self-sustained dynamics of nephrons.

No abstract

It has been known that a diusive coupling between two limit cycle oscillations typically leads to the inphase synchronization and also that it is the only stable state in the weak coupling limit. Recently, however, it has been shown that the coupling of the same nature can result in the distinctive dephased synchronization when the limit cycles are close to the homoclinic bifurcation, which often occurs especially for the neuronal oscillators. In this paper we propose a simple physical model using the modied van der Pol equation, which unfolds the generic synchronization behaviors of the latter kind and in which one may readily observe c hanges in the sychronization behaviors between the distinctive regimes as well. The dephasing mechanism is analyzed both qualitatively and quantitatively in the weak coupling limit. A general form of coupling is introduced and the synchronization behaviors over a wide range of the coupling parameters are explored to construct the phase diagram using the bifurcation analysis. MIRAMARE { TRIESTE September 1998Regular Associate of the Abdus Salam ICTP.