{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T07:13:38Z","timestamp":1767165218312,"version":"build-2238731810"},"reference-count":47,"publisher":"World Scientific Pub Co Pte Ltd","issue":"10","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2000,10]]},"abstract":"<jats:p>Phase synchronized entrainment of coupled nonidentical limit cycles and chaotic oscillators is a generic phenomenon in complicated and chaotic dynamics. Recent developments in phase synchronization are reviewed. Two approaches: The statistical approach and the dynamical approach are proposed. From a statistical viewpoint, phase entrainment exhibits a nonequilibrium phase transition from the disordered state to the ordered state. Dynamically, phase synchronization among oscillators shows a tree-like bifurcation and a number of clustered states are experienced. The route from partial to complete phase synchronization for coupled limit cycles is identified as a cascade of transitions from high- to low-dimensional tori (quasiperiodicity) interrupted by intermittent chaos. For coupled periodic oscillators, desynchronization-induced chaos originates from the mixing of intermittent ON\u2013OFF duration time scales. For coupled chaotic cases, the route to phase entrainment is identified as transitions from high- to low-dimensional chaos.<\/jats:p>","DOI":"10.1142\/s0218127400001535","type":"journal-article","created":{"date-parts":[[2003,4,22]],"date-time":"2003-04-22T07:50:07Z","timestamp":1050997807000},"page":"2399-2414","source":"Crossref","is-referenced-by-count":12,"title":["PHASE SYNCHRONIZATIONS: TRANSITIONS FROM HIGH- TO LOW-DIMENSIONAL TORI THROUGH CHAOS"],"prefix":"10.1142","volume":"10","author":[{"given":"BAMBI","family":"HU","sequence":"first","affiliation":[{"name":"Department of Physics and Center for Nonlinear  Studies, Hong Kong Baptist University, Hong Kong, China"},{"name":"Department of Physics, University of Houston,  TX 77204, USA"}]},{"given":"ZHIGANG","family":"ZHENG","sequence":"additional","affiliation":[{"name":"Department of Physics and Center for Nonlinear  Studies, Hong Kong Baptist University, Hong Kong, China"},{"name":"Department of Physics, Beijing Normal  University, Beijing 100875, China"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.57.5287"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.81.2229"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.82.2800"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.81.3643"},{"key":"p_5","first-page":"321","volume":"115","author":"Carr T. 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