Synchronization in discrete-time networks with general pairwise coupling
Frank Bauer, Fatihcan M. Atay, and Jürgen Jost
Contact the author: Please use for correspondence this email.
Submission date: 10. Sep. 2009
published in: Nonlinearity, 22 (2009) 10, p. 2333-2351
DOI number (of the published article): 10.1088/0951-7715/22/10/001
MSC-Numbers: 05C50, 37D45, 37E05, 39A11
PACS-Numbers: 05.45.-a, 05.45.Ra, 05.45.Xt
Download full preprint: PDF (518 kB)
We consider complete synchronization of identical maps coupled through a general interaction function and in a general network topology where the edges may be directed and may carry both positive and negative weights. We define mixed transverse exponents and derive sufficient conditions for local complete synchronization. The general non-diffusive coupling scheme can lead to new synchronous behavior, in networks of identical units, that cannot be produced by single units in isolation. In particular, we show that synchronous chaos can emerge in networks of simple units. Conversely, in networks of chaotic units simple synchronous dynamics can emerge; that is, chaos can be suppressed through synchrony.