{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T06:42:50Z","timestamp":1740120170618,"version":"3.37.3"},"reference-count":31,"publisher":"World Scientific Pub Co Pte Ltd","issue":"14","funder":[{"DOI":"10.13039\/100010665","name":"H2020 Marie Sk\u0142odowska-Curie Actions","doi-asserted-by":"publisher","award":["675080"],"award-info":[{"award-number":["675080"]}],"id":[{"id":"10.13039\/100010665","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2019,12,30]]},"abstract":"<jats:p> In this paper, a method for pattern analysis in networks of diffusively coupled nonlinear systems of Lur\u2019e form is presented. We consider a class of nonlinear systems which are globally asymptotically stable in isolation. Interconnecting such systems into a network via diffusive coupling can result in persistent oscillatory behavior, which may lead to pattern formation in the coupled systems. Some of these patterns may coexist and can even all be locally stable, i.e. the network dynamics can be multistable. Multistability makes the application of common analysis methods, such as the direct Lyapunov method, highly involved. We develop a numerically efficient method in order to analyze the oscillatory behavior occurring in such networks. We focus on networks of Lur\u2019e systems in which the oscillations appear via a Hopf bifurcation with the (diffusively) coupling strength as a bifurcation parameter and therefore display sinusoidal-like behavior in the neighborhood of the bifurcation point. Using the describing function method, we replace nonlinearities with their linear approximations. Then we analyze the system of linear equations by means of the multivariable harmonic balance method. We show that the multivariable harmonic balance method is able to accurately predict patterns that appear in such a network, even if multiple patterns coexist. <\/jats:p>","DOI":"10.1142\/s0218127419502006","type":"journal-article","created":{"date-parts":[[2019,12,26]],"date-time":"2019-12-26T04:36:48Z","timestamp":1577335008000},"page":"1950200","source":"Crossref","is-referenced-by-count":3,"title":["Pattern Analysis in Networks of Diffusively Coupled Lur\u2019e Systems"],"prefix":"10.1142","volume":"29","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8145-5298","authenticated-orcid":false,"given":"Kirill","family":"Rogov","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, Eindhoven University of Technology, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8755-9832","authenticated-orcid":false,"given":"Alexander","family":"Pogromsky","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Eindhoven University of Technology, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Erik","family":"Steur","sequence":"additional","affiliation":[{"name":"Delft Center for Systems and Control, Delft University of Technology, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0877-0080","authenticated-orcid":false,"given":"Wim","family":"Michiels","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Catholic University of Leuven, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5883-6191","authenticated-orcid":false,"given":"Henk","family":"Nijmeijer","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Eindhoven University of Technology, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2019,12,26]]},"reference":[{"key":"S0218127419502006BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/S0362-546X(97)00020-5"},{"key":"S0218127419502006BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/PL00011391"},{"key":"S0218127419502006BIB003","doi-asserted-by":"publisher","DOI":"10.1142\/2446"},{"key":"S0218127419502006BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/0771-050X(80)90013-3"},{"key":"S0218127419502006BIB005","volume-title":"Abstract Algebra","author":"Dummit D. 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