Synchronization of strange nonchaotic attractors

Abstract

Strange nonchaotic attractors (SNAs), which are realized in many quasiperiodically driven nonlinear systems, are strange (geometrically fractal) but nonchaotic (the largest nontrivial Lyapunov exponent is negative). Two such identical independent systems can be synchronized by in-phase driving: Because of the negative Lyapunov exponent, the systems converge to a common dynamics, which, because of the strangeness of the underlying attractor, is aperiodic. This feature, which is robust to external noise, can be used for applications such as secure communication. A possible implementation is discussed and its performance is evaluated. The use of SNAs rather than chaotic attractors can offer some advantages in experiments involving synchronization with aperiodic dynamics.