{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T03:52:23Z","timestamp":1743047543585,"version":"3.40.3"},"publisher-location":"Cham","reference-count":25,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030781620"},{"type":"electronic","value":"9783030781637"}],"license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021]]},"DOI":"10.1007\/978-3-030-78163-7_14","type":"book-chapter","created":{"date-parts":[[2021,9,29]],"date-time":"2021-09-29T06:14:35Z","timestamp":1632896075000},"page":"323-354","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Synchronisation of Weakly Coupled Oscillators"],"prefix":"10.1007","author":[{"given":"Rog\u00e9rio","family":"Martins","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,9,30]]},"reference":[{"key":"14_CR1","unstructured":"Birkhoff, G., Rota, G.-C.: Ordinary Differential Equations, 4th edn. Wiley, New York (1989)"},{"key":"14_CR2","volume-title":"The Pendulum, a Case Study in Physics","author":"GL Baker","year":"2005","unstructured":"Baker, G.L., Blackburn, J.A.: The Pendulum, a Case Study in Physics. Press, Oxford Uni (2005)"},{"key":"14_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0370-1573(02)00137-0","volume":"366","author":"S Boccaletti","year":"2002","unstructured":"Boccaletti, S., Kurths, J., Osipov, G., Valladares, D.L., Zhou, C.S.: The Syncronization of Chaotic Systems. Physics Reports 366, 1\u201310 (2002)","journal-title":"Phys. Rep."},{"key":"14_CR4","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1090\/qam\/484023","volume":"36","author":"FC Hoppensteadt","year":"1978","unstructured":"Hoppensteadt, F.C., Levi, M., Miranker, W.L.: Dynamics of the Josephson Junction. Quart. Appl. Math. 36, 167\u2013198 (1978)","journal-title":"Q. Appl. Math."},{"key":"14_CR5","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511840371","volume-title":"Topics in Matrix Analysis","author":"R Horn","year":"1991","unstructured":"Horn, R., Johnson, C.: Topics in Matrix Analysis. Press, Cambridge Uni (1991)"},{"key":"14_CR6","doi-asserted-by":"publisher","first-page":"2933","DOI":"10.1016\/j.physd.2008.04.015","volume":"237","author":"G Katriel","year":"2008","unstructured":"Katriel, G.: Synchronization of Oscillators Coupled Through an Environment. Physica D 237, 2933\u20132944 (2008)","journal-title":"Phys. D"},{"key":"14_CR7","unstructured":"Lax, P.: Linear Algebra. Wiley, New York (1997)"},{"key":"14_CR8","doi-asserted-by":"publisher","first-page":"927","DOI":"10.1103\/PhysRevA.37.927","volume":"37","author":"M Levi","year":"1988","unstructured":"Levi, M.: Nonchaotic Behavior in the Josephson Junction. Physical Review A 37, 927\u2013931 (1988)","journal-title":"Phys. Rev. A"},{"key":"14_CR9","doi-asserted-by":"publisher","first-page":"351","DOI":"10.1016\/j.jde.2004.07.012","volume":"212","author":"R Martins","year":"2005","unstructured":"Martins, R.: The Effect of Inversely Unstable Solutions on the Attractor of the Forced Pendulum Equation With Friction. J. Differential Equations 212, 351\u2013365 (2005)","journal-title":"J. Differ. Equs."},{"key":"14_CR10","doi-asserted-by":"publisher","first-page":"533","DOI":"10.3934\/dcds.2006.14.533","volume":"14","author":"R Martins","year":"2006","unstructured":"Martins, R.: One-dimensional Attractor for a Dissipative System With a Cylindrical Phase Space. Discrete and Continuous Dynamical Systems-Series A 14, 533\u2013547 (2006)","journal-title":"Discret. Contin. Dyn. Syst.-Ser. A"},{"key":"14_CR11","doi-asserted-by":"publisher","first-page":"1265","DOI":"10.1016\/j.jmaa.2008.01.017","volume":"342","author":"R Martins","year":"2008","unstructured":"Martins, R.: The Attractor of an Equation of Tricomi\u2019s Type. J. Math. Anal. Appl. 342, 1265\u20131270 (2008)","journal-title":"J. Math. Anal. Appl."},{"key":"14_CR12","doi-asserted-by":"publisher","first-page":"3215","DOI":"10.1016\/j.jde.2010.09.005","volume":"249","author":"A Margheri","year":"2010","unstructured":"Margheri, A., Martins, R.: Generalized Synchronization in Linearly Coupled Time Periodic Systems. Journal of Differential Equations 249, 3215\u20133232 (2010)","journal-title":"J. Differ. Equs."},{"key":"14_CR13","first-page":"347","volume":"51","author":"R Martins","year":"2015","unstructured":"Martins, R., Morais, G.: Generalized Synchronization in a System of Several Non-autonomous Oscillators Coupled by a M\u00e9dium. Kybernetika 51, 347\u2013373 (2015)","journal-title":"Kybernetika"},{"key":"14_CR14","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1016\/0022-0396(88)90030-7","volume":"71","author":"Q Min","year":"1988","unstructured":"Min, Q., Xian, S., Jinyan, Z.: Global Behavior in the Dynamical Equation of J-J type. J. Differential Equations 71, 315\u2013333 (1988)","journal-title":"J. Differ. Equs."},{"key":"14_CR15","doi-asserted-by":"publisher","first-page":"992","DOI":"10.1119\/1.1501118","volume":"70","author":"J Pantaleone","year":"2002","unstructured":"Pantaleone, J.: Synchronization of Metronomes. Am. J. Phys. 70, 992\u20131000 (2002)","journal-title":"Am. J. Phys."},{"key":"14_CR16","doi-asserted-by":"publisher","first-page":"520","DOI":"10.1063\/1.166278","volume":"7","author":"L Pecora","year":"1997","unstructured":"Pecora, L., Carroll, T., Johnson, G., Mar, D., Heagy, J.: Fundamentals of Synchronization in Chaotic Systems, Concepts, and Applications. Chaos 7, 520\u2013543 (1997)","journal-title":"Chaos"},{"key":"14_CR17","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41598-016-0001-8","volume":"6","author":"J Ramirez","year":"2016","unstructured":"Ramirez, J., Olvera, L., Nijmeijer, H., Alvarez, J.: The Sympathy of Two Pendulum Clocks: Beyond Huygens Observations. Scientific Reports 6, 1\u201316 (2016)","journal-title":"Sci. Rep."},{"key":"14_CR18","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1112\/jlms\/s2-7.2.203","volume":"7","author":"RA Smith","year":"1973","unstructured":"Smith, R.A.: Absolute Stability of Certain Differential Equations. J. London Math. Soc. 7, 203\u2013210 (1973)","journal-title":"J. Lond. Math. Soc."},{"key":"14_CR19","doi-asserted-by":"publisher","first-page":"679","DOI":"10.1016\/0022-247X(86)90189-7","volume":"120","author":"RA Smith","year":"1986","unstructured":"Smith, R.A.: Massera\u2019s Convergence Theorem for Periodic Nonlinear Differential Equations. J. Math. Anal. Appl. 120, 679\u2013708 (1986)","journal-title":"J. Math. Anal. Appl."},{"key":"14_CR20","unstructured":"Sobel D.: Longitude: the true story of a lone genius who solved the greatest scientific problem of his time. Walker & Company (1995)"},{"key":"14_CR21","doi-asserted-by":"crossref","unstructured":"Srzednicki, R.: Wazewski method and Conley index. In: Handbook of Differential Equations, pp. 591\u2013684. Elsevier\/North-Holland, Amsterdam (2004)","DOI":"10.1016\/S1874-5725(00)80009-7"},{"key":"14_CR22","unstructured":"Strogatz, S.: Sync. The Emerging Science Of Spontaneous Order. Penguin (2004)"},{"key":"#cr-split#-14_CR23.1","unstructured":"Wazewski, T.: Sur une M\u00e9thode Topologique de l'Examen de l'Allure Asymptotique des Int\u00e9grales des \u00c9quations Diff\u00e9rentielles. In: Proceedings of the International Congress of Mathematicians, 1954, Amsterdam, vol. III, pp. 132-139. Erven P. Noordhoff N.V., Groningen"},{"key":"#cr-split#-14_CR23.2","unstructured":"North-Holland Publishing Co., Amsterdam (1956)"},{"key":"14_CR24","doi-asserted-by":"crossref","unstructured":"Wu, C.W., Chua, L.O.: Synchronization in an array of linearly coupled dynamical systems. IEEE Trans. Circuits Syst.-I: Fundam. Theory Appl. 42, 430\u2013447 (1995)","DOI":"10.1109\/81.404047"}],"container-title":["Springer Proceedings in Mathematics & Statistics","Modeling, Dynamics, Optimization and Bioeconomics IV"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-78163-7_14","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,29]],"date-time":"2021-09-29T06:47:47Z","timestamp":1632898067000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-78163-7_14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"ISBN":["9783030781620","9783030781637"],"references-count":25,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-78163-7_14","relation":{},"ISSN":["2194-1009","2194-1017"],"issn-type":[{"type":"print","value":"2194-1009"},{"type":"electronic","value":"2194-1017"}],"subject":[],"published":{"date-parts":[[2021]]},"assertion":[{"value":"30 September 2021","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}