Realization of the hyperbolic chaos and complex analytical dynamics in one ring stage wave system

O.B. Isaeva, M.A. Obychev, S.P. Kuznetsov

Saratov State University, Russia

In the present work we propose the system in which the hyperbolic chaos, associated with Smale–Williams attractor and Bernoulli map, and the phenomena of complex analytical dynamics, associated with quadratic Mandelbrot map, can be realized. The system contain the nonlinear elements, which can be described by the classical model of two wave interaction. Methodology of construction of such system is based on the phase and amplitude manipulation of the signal in the ring. Numerical verification of the hyperbolicity and complex analycity are carried out.