Experimental Study of the Transitions between Synchronous Chaos and a Periodic Rotating Wave

Abstract

The transition between periodic rotating waves and synchronized chaos in a ring of unidirectionally coupled Lorenz oscillators is experimentally investigated by means of electronic circuits. The study is complemented by means of numerical and theoretical analysis. The intermediate states and their transitions are identified. The route linking periodic behavior with synchronous chaos involves two- and three-frequency quasiperiodicity and a type of high-dimensional chaos known as chaotic rotating wave. The 3D-torus exists in a finite parameter region robustly, and has been experimentally observed and characterized with the aid of Fourier analysis and the Poincaré cross section technique. The high-dimensional chaotic behavior is also characterized, and is shown to be composed actually by three different behaviors. Very good agreement is found in all the transitions between the experimental results and the corresponding numerical analysis of the model.