Limits to the Experimental Detection of Nonlinear Synchrony

Paul So, Ernest Barreto, Kresimir Josic, Evelyn Sander, and Steven J. Schiff

Chaos synchronization is often characterized by the existence of a continuous function between the states
of the components. However, in coupled systems without inherent symmetries, the synchronization set might
be extremely complicated. For coupled invertible systems, the synchronization set can be nondifferentiable;
in the more severe case of coupled noninvertible systems, the synchronization set will in general be a
multivalued relation. We will discuss how existing methods for detecting synchronization will be hampered
by these features.