{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:26:51Z","timestamp":1787232411526,"version":"3.56.0"},"reference-count":19,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Dyn. Syst."],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.1137\/060652531","type":"journal-article","created":{"date-parts":[[2006,10,2]],"date-time":"2006-10-02T18:11:50Z","timestamp":1159812710000},"page":"508-527","source":"Crossref","is-referenced-by-count":43,"title":["Stability of Coupled Map Networks with Delays"],"prefix":"10.1137","volume":"5","author":[{"given":"Fatihcan M.","family":"Atay","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"\u00d6zkan","family":"Karabacak","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,9,26]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1143\/PTP.72.480"},{"key":"R2","unstructured":"K. Kaneko,\n                      Theory and Applications of Coupled Map Lattices\n                      , Wiley, New York, 1993."},{"key":"R3","doi-asserted-by":"crossref","unstructured":"A. Pikovsky, M. Rosenblum, and J. Kurths,\n                      Synchronization\u2014A Universal Concept in Nonlinear Science\n                      , Cambridge University Press, Cambridge, UK, 2001.","DOI":"10.1017\/CBO9780511755743"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.64.821"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.65.016201"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.92.144101"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.80.5109"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(03)00154-4"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(85)90182-4"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(90)90007-C"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2005.01.007"},{"key":"R12","unstructured":"S. Elaydi,\n                      An Introduction to Difference Equations\n                      , 3rd ed., Springer, New York, 2005."},{"key":"R13","unstructured":"F. R. K. Chung,\n                      Spectral Graph Theory\n                      , American Mathematical Society, Providence, RI, 1997."},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1080\/00207170110107265"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-45606-6_7"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2001.1.233"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.91.094101"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1007\/BF00275067"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1994.1457"}],"container-title":["SIAM Journal on Applied Dynamical Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/060652531","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T12:48:54Z","timestamp":1787230134000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/060652531"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1]]},"references-count":19,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2006,1]]}},"alternative-id":["10.1137\/060652531"],"URL":"https:\/\/doi.org\/10.1137\/060652531","relation":{},"ISSN":["1536-0040"],"issn-type":[{"value":"1536-0040","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,1]]}}}