Michael E. Henderson
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
We study synchronization in an array of coupled identical nonlinear dynamical systems where the coupling topology is expressed as a directed graph and give synchronization criteria related to properties of a generalized Laplacian matrix of the directed graph. In particular, we extend recent results by showing that the array synchronizes for sufficiently large cooperative coupling if the underlying graph contains a spanning directed tree. This is an intuitive yet nontrivial result that can be paraphrased as follows: if there exists a dynamical system which influences directly or indirectly all other systems, then synchronization is possible for strong enough coupling. The converse is also true in general. © 2005 IOP Publishing Ltd and London Mathematical Society.
Michael E. Henderson
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Richard M. Karp, Raymond E. Miller
Journal of Computer and System Sciences
Jonathan Ashley, Brian Marcus, et al.
Ergodic Theory and Dynamical Systems
Andrew Skumanich
SPIE Optics Quebec 1993