Chaos synchronization and hyperchaos

Abstract

We discuss the relation between phenomena of chaos synchronization in coupled systems and creation of hyperchaotic attractors (attractors with at least two positive Lyapunov exponents. Such attractors are common in higher-dimensional dynamical systems (at least two-dimensional maps or four-dimensional flows). Riddling bifurcation i.e., the bifurcation in which one of the unstable periodic orbits embedded in a chaotic attractor located on the invariant manifold becomes unstable transversely to the attractor leads to the loss of chaos synchronization in coupled identical systems. We show that generalized riddling bifurcation defined as the bifurcation in which one of the unstable periodic orbits embedded in a higher-dimensional chaotic attractor (not necessarily located on the invariant manifold) becomes unstable transversely to the attractor explains mechanism of the creation of hyperchaotic attractors. Additionally we show that the generalized riddling bifurcation can give physical mechanism explaining interstellar journeys described in science-fiction literature. © 2005 IOP Publishing Ltd.