{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,10]],"date-time":"2026-10-10T00:20:31Z","timestamp":1791591631397,"version":"4.3.4"},"reference-count":41,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2003,4]]},"abstract":"<jats:p>Cluster synchronization modes of continuous time oscillators that are diffusively coupled in a three-dimensional (3-D) lattice are studied in the paper via the corresponding linear invariant manifolds. Depending in an essential way on the number of oscillators composing the lattice in three volume directions, the set of possible regimes of spatiotemporal synchronization is examined. Sufficient conditions of the stability of cluster synchronization are obtained analytically for a wide class of coupled dynamical systems with complicated individual behavior. Dependence of the necessary coupling strengths for the onset of global synchronization on the number of oscillators in each lattice direction is discussed and an approximative formula is proposed. The appearance and order of stabilization of the cluster synchronization modes with increasing coupling between the oscillators are revealed for 2-D and 3-D lattices of coupled Lur'e systems and of coupled R\u00f6ssler oscillators.<\/jats:p>","DOI":"10.1142\/s0218127403006923","type":"journal-article","created":{"date-parts":[[2003,6,17]],"date-time":"2003-06-17T12:04:14Z","timestamp":1055851454000},"page":"755-779","source":"Crossref","is-referenced-by-count":47,"title":["CLUSTER SYNCHRONIZATION IN THREE-DIMENSIONAL LATTICES OF DIFFUSIVELY COUPLED OSCILLATORS"],"prefix":"10.1142","volume":"13","author":[{"given":"VLADIMIR N.","family":"BELYKH","sequence":"first","affiliation":[{"name":"Mathematics Department, Volga State Academy, 5, Nesterov St., Nizhny Novgorod, 603 600, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"IGOR V.","family":"BELYKH","sequence":"additional","affiliation":[{"name":"Laboratory of Nonlinear Systems, School of Computer and Communication Sciences, Swiss Federal Institute of Technology (EPFL), CH-1015 Lausanne, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"MARTIN","family":"HASLER","sequence":"additional","affiliation":[{"name":"Laboratory of Nonlinear Systems, School of Computer and Communication Sciences, Swiss Federal Institute of Technology (EPFL), CH-1015 Lausanne, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"KONSTANTIN V.","family":"NEVIDIN","sequence":"additional","affiliation":[{"name":"Volga State Academy, 5, Nesterov St., Nizhny Novgorod, 603 600, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01034476"},{"key":"rf2","first-page":"445","volume":"103","author":"Afraimovich V. S.","journal-title":"Physica D"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127492000446"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(94)90947-4"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/9\/3\/006"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1142\/S0218126693000356"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.54.3196"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.62.6332"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.63.036216"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1063\/1.1514202"},{"key":"rf11","first-page":"1310","volume":"38","author":"Bel'skii Yu. L.","journal-title":"Radiotechn. Elektron."},{"key":"rf12","volume-title":"Controlling Chaos and Bifurcations in Engineering Systems","author":"Chen G.","year":"2000"},{"key":"rf13","doi-asserted-by":"crossref","first-page":"2717","DOI":"10.1142\/S0218127400001778","volume":"10","author":"Chiu C. H.","journal-title":"Int. J. Bifurcation and Chaos"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1109\/81.473583"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1109\/31.7600"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1109\/81.473564"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127497001618"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.61.5080"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1142\/3412"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1143\/PTP.69.32"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.1995.0094"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.58.6843"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.50.1874"},{"key":"rf24","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.80.3956"},{"key":"rf25","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/13\/4\/318"},{"key":"rf26","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(90)90119-A"},{"key":"rf27","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.63.016212"},{"key":"rf28","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.82.1140"},{"key":"rf29","doi-asserted-by":"publisher","DOI":"10.1142\/1997"},{"key":"rf30","doi-asserted-by":"publisher","DOI":"10.1109\/81.473584"},{"key":"rf31","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(96)00202-3"},{"key":"rf32","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.64.821"},{"key":"rf33","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.58.347"},{"key":"rf34","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.80.2109"},{"key":"rf35","doi-asserted-by":"publisher","DOI":"10.1109\/81.904879"},{"key":"rf36","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.60.R1130"},{"key":"rf37","first-page":"811","volume":"56","author":"Sherman A.","journal-title":"Bull. Math. Biol."},{"key":"rf38","doi-asserted-by":"publisher","DOI":"10.1109\/81.473585"},{"key":"rf39","volume-title":"Dynamics and Self-Organization of Locally Coupled Neural Networks","author":"Thiran P.","year":"1997"},{"key":"rf40","first-page":"161","volume":"43","author":"Wu C. W.","journal-title":"IEEE Trans. Circuits Syst.-I"},{"key":"rf41","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.55.79"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127403006923","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,3,21]],"date-time":"2020-03-21T21:09:40Z","timestamp":1584824980000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127403006923"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,4]]},"references-count":41,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2003,4]]}},"alternative-id":["10.1142\/S0218127403006923"],"URL":"https:\/\/doi.org\/10.1142\/s0218127403006923","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,4]]}}}