The geometry of chaos synchronization.
Chaos synchronization in coupled systems is often characterized by a map phi between the states of the components. In noninvertible systems, or in systems without inherent symmetries, the synchronization set--by which we mean graph(phi)--can be extremely complicated. We identify, describe, and give examples of several different complications that can arise, and we link each to inherent properties of the underlying dynamics. In brief, synchronization sets can in general become nondifferentiable, and in the more severe case of noninvertible dynamics, they might even be multivalued. We suggest two different ways to quantify these features, and we discuss possible failures in detecting chaos synchrony using standard continuity-based methods when these features are present.
Barreto
Ernest
E
Department of Physics and Astronomy and the Krasnow Institute for Advanced Study, George Mason University, Fairfax, Virginia 22030, USA.
Josić
Kresimir
K
Morales
Carlos J
CJ
Sander
Evelyn
E
So
Paul
P
D000465:Algorithms; D000818:Animals; D008962:Models, Theoretical; D009474:Neurons / Q000502:physiology*; D017711:Nonlinear Dynamics; D055585:Physical Phenomena; D010825:Physics