Collective phase locked states in a chain of coupled chaotic oscillators

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.

Chaotic synchronization of coupled electron-wave systems with backward waves

The chaotic synchronization of two electron-wave media with interacting backward waves and cubic phase nonlinearity is investigated in the paper. To detect the chaotic synchronization regime we use a new approach, the so-called time scale synchronization [Chaos 14, 603-610 (2004)]. This approach is based on the consideration of the infinite set of chaotic signals' phases introduced by means of continuous wavelet transform. The complex space-time dynamics of the active media and mechanisms of the time scale synchronization appearance are considered.

Convective instabilities of synchronization manifolds in spatially extended systems

We study the stability properties of anticipating synchronization in an open chain of unidirectionally coupled identical chaotic oscillators. Despite being absolutely stable, the synchronization manifold is unstable to propagating perturbations. We analyze and characterize such instabilities drawing a qualitative and quantitative comparison with the convective instabilities typical of spatially extended systems.

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.

Phase synchronization and topological defects in inhomogeneous media

The influence of topological defects on phase synchronization and phase coherence in two-dimensional arrays of locally coupled, nonidentical, chaotic oscillators is investigated. The motion of topological defects leads to a breakdown of phase synchronization in the vicinities of the defects; however, the system is much more phase coherent as long as the coupling between the oscillators is strong enough to prohibit the continuous dynamical creation and annihilation of defects. The generic occurrence of topological defects in two and higher dimensions implies that the concept of phase synchronization has to be modified for these systems.