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The node couplings are assumed to be linear but with switching directed communication graphs. Several sufficient and\/or necessary conditions are established for exact or approximate synchronization over the considered complex networks. These results show when and how nonlinear node self-dynamics may cooperate with the linear diffusive coupling, which eventually leads to network synchronization conditions under relaxed connectivity requirements.<\/jats:p>","DOI":"10.1137\/130950811","type":"journal-article","created":{"date-parts":[[2015,12,9]],"date-time":"2015-12-09T02:19:02Z","timestamp":1449627542000},"page":"3562-3583","source":"Crossref","is-referenced-by-count":11,"title":["Network Synchronization with Convexity"],"prefix":"10.1137","volume":"53","author":[{"given":"Guodong","family":"Shi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexandre","family":"Proutiere","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Karl Henrik","family":"Johansson","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,12,8]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"J. 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