SIAM Digital Library
 
 
 

You are not logged in Logged Out Log In

SIAM J. on Applied Dynamical Systems / Volume 5 / Issue 3

SIAM J. Appl. Dyn. Syst. 5, pp. 508-527 (20 pages)

Stability of Coupled Map Networks with Delays

Fatihcan M. Atay and Özkan Karabacak

Full Text: Download PDF | Buy PDF (US$25) | View Cart
We consider networks of coupled scalar maps, with weighted connections which may include a time delay, and study the stability of equilibria with respect to the delays and connection structure. We prove that the largest eigenvalue of the graph Laplacian determines the effect of the connection topology on stability. The stability region in the parameter plane shrinks with increasing values of the largest eigenvalue, or of the time delay of the same parity. In particular, all bipartite graphs have an identical stability region, regardless of the delay or graph size, which is also the smallest stability region among those of all graphs. Furthermore, for certain parameter ranges, unstable (and possibly chaotic) maps can be stabilized via diffusive coupling with an odd time delay, provided that the network does not have a nontrivial and connected bipartite component. On the other hand, stabilization is not possible for even values of the delay or for bipartite networks.

© 2006 Society for Industrial and Applied Mathematics

RELATED DATABASES

To view database links for this article, you need to log in.

KEYWORDS

AMS Subject Headings

39A11, 37E05, 94C15

PUBLICATION DATA

ISSN:

1536-0040 (print)  
1536-0040 (online)

Publisher:

$abstract.society.value is a Member of CrossRef Society for Industrial and Applied Mathematics

ARTICLE DATA

History
Received February 20, 2006
Accepted April 28, 2006
Published online September 26, 2006
Permalink
http://dx.doi.org/10.1137/060652531

For access to fully linked references, you need to log in.

For access to citing articles, you need to log in.


Close

Your Recent History Recent History Help

Recently Viewed

  1. Stability of Coupled Map Networks with Delays
  2. Statistically Hiding Commitments and Statistical Zero-Knowledge Arguments from Any One-Way Function
© SIAM By using SIAM Publications Online you agree to abide by the Terms and Conditions of Use. Banner art adapted from a figure by Hinke M. Osinga and Bernd Krauskopf (University of Bristol, UK).
close