Loss of synchronization in coupled oscillators with ubiquitous local stability.
The issue of using instantaneous eigenvalues as indicators of synchronization quality in coupled chaotic systems is examined. Previously, it has been assumed that, if the eigenvalues of the linearized synchronization dynamics have negative real parts everywhere on the attractor, the synchronized state is stable. In this Rapid Communication, two counterexamples are presented that show this assumption is invalid.
Corron
N J
NJ
U.S. Army Aviation and Missile Command, AMSAM-RD-WS-ST, Redstone Arsenal, Alabama 35898, USA. ned.corron@ws.redstone.army.mil