Random maps in physical systemsL. Trujillo1, 2, 3, J. J. Suárez3 and J. A. González2, 3
1 PMMH (CNRS UMR 7636), ESPCI - 10 rue Vauquelin, 75231 Paris Cedex 05, France
2 International Centre for Theoretical Physics (ICTP) - Trieste, Italy
3 Centro de Física, IVIC - A.P. 21827, Caracas 1020-A, Venezuela
(Received 12 January 2004; accepted in final form 25 March 2004)
We show that functions of type Xn=P[Zn], where P[t] is a periodic function and Z is a generic real number, can produce sequences such that any string of values is deterministically independent of past and future values. There are no correlations between any values of the sequence. We show that this kind of dynamics can be generated using a recently constructed optical device composed of several Mach-Zehnder interferometers. Quasiperiodic signals can be transformed into random dynamics using nonlinear circuits. We present the results of real experiments with nonlinear circuits that simulate exponential and sine functions.
05.45.-a - Nonlinear dynamics and nonlinear dynamical systems.
42.65.Sf - Dynamics of nonlinear optical systems; optical instabilities, optical chaos and complexity, and optical spatio-temporal dynamics.
05.45.Vx - Communication using chaos.
© EDP Sciences 2004