{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:11:28Z","timestamp":1787321488382,"version":"3.56.0"},"reference-count":37,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Math. Anal."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>We study the local complete synchronization of discrete-time dynamical networks with time-varying couplings. Our conditions for the temporal variation of the couplings are rather general and include variations in both the network structure and the reaction dynamics; the reactions could, for example, be driven by a random dynamical system. A basic tool is the concept of the Hajnal diameter, which we extend to infinite Jacobian matrix sequences. The Hajnal diameter can be used to verify synchronization, and we show that it is equivalent to other quantities which have been extended to time-varying cases, such as the projection radius, projection Lyapunov exponents, and transverse Lyapunov exponents. Furthermore, these results are used to investigate the synchronization problem in coupled map networks with time-varying topologies and possibly directed and weighted edges. In this case, the Hajnal diameter of the infinite coupling matrices can be used to measure the synchronizability of the network process. As we show, the network is capable of synchronizing some chaotic map if and only if there exists an integer $T&gt;0$ such that for any time interval of length T, there exists a vertex which can access other vertices by directed paths in that time interval.<\/jats:p>","DOI":"10.1137\/060657935","type":"journal-article","created":{"date-parts":[[2007,11,30]],"date-time":"2007-11-30T18:12:17Z","timestamp":1196446337000},"page":"1231-1259","source":"Crossref","is-referenced-by-count":77,"title":["Synchronization of Discrete-Time Dynamical Networks with Time-Varying Couplings"],"prefix":"10.1137","volume":"39","author":[{"given":"Wenlian","family":"Lu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fatihcan M.","family":"Atay","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J\u00fcrgen","family":"Jost","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2007,11,30]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/9\/3\/006"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01212280"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"A. Pikovsky, M. Rosenblum, and J. Kurths,\n                      Synchronization: A Universal Concept in Nonlinear Sciences\n                      , Cambridge University Press, Cambridge, UK, 2001.","DOI":"10.1017\/CBO9780511755743"},{"key":"R4","unstructured":"K. Kaneko,\n                      Theory and Applications of Coupled Map Lattices\n                      , Wiley, New York, 1993."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.65.016201"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.67.026209"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.92.144101"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2004.08.024"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/18\/3\/007"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1109\/TCSII.2006.886236"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2004.834113"},{"key":"R12","unstructured":"Y. Hatano and M. Mesbahi,\n                      Agreement over random networks\n                      , in Proceedings of the IEEE Conference on Decision and Control, 2004; available online from http:\/\/www.aa.washington.edu\/faculty\/mesbahi\/papers\/random-cdc.pdf."},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.75.1226"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2004.841888"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2005.849233"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2004.03.012"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1137\/050625229"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100033399"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100030991"},{"key":"R20","unstructured":"J. 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