Phase synchronization of chaotic attractors in the presence of two competing periodic signals

Detecting couplings between interacting oscillators with time-varying basic frequencies: instantaneous wavelet bispectrum and information theoretic approach

In the natural world, the properties of interacting oscillatory systems are not constant, but evolve or fluctuating continuously in time. Thus, the basic frequencies of the interacting oscillators are time varying, which makes the system analysis complex. For studying their interactions we propose a complementary approach combining wavelet bispectral analysis and information theory. We show how these methods uncover the interacting properties and reveal the nature, strength, and direction of coupling. Wavelet bispectral analysis is generalized as a technique for detecting instantaneous phase-time dependence for the case of two or more coupled nonlinear oscillators whereas the information theory approach can uncover the directionality of coupling and extract driver-response relationships in complex systems. We generate bivariate time-series numerically to mimic typical situations that occur in real measured data, apply both methods to the same time-series and discuss the results. The approach is applicable quite generally to any system of coupled nonlinear oscillators.

Wavelet bispectral analysis for the study of interactions among oscillators whose basic frequencies are significantly time variable

Bispectral analysis, recently introduced as a technique for revealing time-phase relationships, is extended to make use of wavelets rather than Fourier analysis. It is thus able to encompass instantaneous phase-time dependence for the case of two or more coupled nonlinear oscillators. The method is demonstrated and evaluated by use of test signals from a pair of coupled Poincaré oscillators. It promises to be useful in a wide range of scientific contexts for studies of interacting oscillators whose basic frequencies are significantly time variable.

Property change of unstable fixed point and phase synchronization in controlling spatiotemporal chaos by a periodic signal

Mechanisms for the suppression of spatiotemporal chaos (STC) in one-dimensional driven drift-wave system to a spatially regular state by a periodic signal are investigated. In the driving wave coordinate, by transforming the system to a set of coupled oscillators (modes) moving in a periodic potential, it is found that the modes can be enslaved one by one through phase synchronization (PS) by the control signal; for some modes frequency-locking occurs while the other modes display multilooping PS without frequency-locking. Further study of the linear behavior of the modes shows that the saddle point embedded in the STC is changed to an unstable focus, which makes it possible for the imperfect PS to change to a perfect functional one, leading to the suppression of the STC.

Experimental observation of synchronous competition in the Chua system

We present experimental results for two different sinusoidal functions competing to phase synchronize a Chua oscillator. Our approach involves real-time observation of the synchronization process. It shows that depending on the amplitude and frequency values of the two sinusoidal functions, the Chua oscillator can stay phase synchronized to one or the other of the inputs all the time or can alternate synchronous states between them. Numerical simulations show good agreement with the experimental observations.

Competition of synchronization domains in arrays of chaotic homoclinic systems

We investigate the response of an open chain of bidirectionally coupled chaotic homoclinic systems to external periodic stimuli. When one end of the chain is driven by a periodic signal, the system propagates a phase synchronization state in a certain range of coupling strengths and external frequencies. When two simultaneous forcings are applied at different points of the array, a rich phenomenology of stable competitive states is observed, including temporal alternation and spatial coexistence of synchronization domains.

Phase synchronization of chaotic attractors with prescribed periodic signals

Given a chaotic attractor in a dynamical system with dense periodic windows (i.e., structurally unstable), is it possible to find a periodic driver that will phase synchronize the chaotic attractor? We conjecture that the answer is typically yes, and we give an example for a funneling chaotic attractor in the Roessler system.

Experimental Chua-plasma phase synchronization of chaos

Experimental phase synchronization of chaos is demonstrated for two different chaotic oscillators: a plasma discharge and the Chua circuit. Our technique includes real-time capability for observing synchronization-desynchronization transitions. This capability results from a strong combination of synchronization and control, and allows tuning adjustments for search and stabilization of synchronous states. A power law is observed for the mean time between 2pi phase slips for different coupling strenghts. The experimental results are consistent with the numerical simulations.

Competition between two frequencies for phase synchronization of a chaotic laser

Competition between two distinct driving frequencies to phase synchronize the intensity dynamics of a chaotic laser has been observed. The phase of the chaotic intensity signal is constructed using the complex analytic signal. Competing frequencies alternately show phase locking and phase slipping. Competition has been quantified by calculating the portion of time the laser phase locks to each of the driving frequencies and their average.