{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T03:45:20Z","timestamp":1771645520544,"version":"3.50.1"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2014,6,26]],"date-time":"2014-06-26T00:00:00Z","timestamp":1403740800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Nonlinear Dyn"],"published-print":{"date-parts":[[2014,10]]},"DOI":"10.1007\/s11071-014-1512-0","type":"journal-article","created":{"date-parts":[[2014,6,25]],"date-time":"2014-06-25T13:25:41Z","timestamp":1403702741000},"page":"1245-1259","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Exciting dynamical behavior in a network of two coupled rings of Chen oscillators"],"prefix":"10.1007","volume":"78","author":[{"given":"Carla M. A.","family":"Pinto","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,6,26]]},"reference":[{"key":"1512_CR1","doi-asserted-by":"crossref","first-page":"033108","DOI":"10.1063\/1.4813227","volume":"23","author":"A Algaba","year":"2013","unstructured":"Algaba, A., Fern\u00e1ndez-S\u00e1nchez, F., Merino, M., Rodr\u00edguez-Luis, A.J.: Chen\u2019s attractor exists if Lorenz repulsor exists: the Chen system is a special case of the Lorenz system. Chaos An Interdiscip. J. Nonlinear Sci. 23, 033108 (2013)","journal-title":"Chaos An Interdiscip. J. Nonlinear Sci."},{"issue":"15","key":"1512_CR2","doi-asserted-by":"crossref","first-page":"1048","DOI":"10.1016\/j.cnsns.2009.05.035","volume":"15","author":"F Antoneli","year":"2010","unstructured":"Antoneli, F., Dias, A.P.S., Pinto, C.M.A.: Quasi-periodic states in coupled rings of cells. Commun. Nonlinear Sci. Numer. Simul. 15(15), 1048\u20131062 (2010)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"1512_CR3","unstructured":"Antoneli, F., Dias, A.P.S., Pinto, C.M.A.: Rich phenomena in a network of two ring coupled through a \u2018buffer\u2019 cell. In: Proceedings of the 2nd Conference on Nonlinear Science and Complexity NSC2008 (2008)"},{"key":"1512_CR4","unstructured":"Antoneli, F., Dias, A.P.S., Pinto, C.M.A.: New phenomena in coupled rings of cells. In: Proceedings of the 3rd IFAC Workshop on Fractional Differentiation and its Applications FDA2008 (2008)"},{"key":"1512_CR5","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/0375-9601(94)90947-4","volume":"193","author":"P Ashwin","year":"1994","unstructured":"Ashwin, P., Buescu, J., Stewart, I.: Bubbling of attractors and synchronisation of oscillators. Phys. Lett. A 193, 126\u2013139 (1994)","journal-title":"Phys. Lett. A"},{"issue":"4","key":"1512_CR6","doi-asserted-by":"crossref","first-page":"454","DOI":"10.1016\/j.physd.2007.09.015","volume":"237","author":"P Ashwin","year":"2008","unstructured":"Ashwin, P., Burylko, O., Maistrenko, Y.: Bifurcation to heteroclinic cycles and sensitivity in three and four coupled phase oscillators. Phys. D 237(4), 454\u2013466 (2008)","journal-title":"Phys. D"},{"key":"1512_CR7","doi-asserted-by":"crossref","first-page":"739","DOI":"10.1088\/0951-7715\/14\/4\/305","volume":"14","author":"PC Bressloff","year":"2001","unstructured":"Bressloff, P.C., Cowan, J.D., Golubitsky, M., Thomas, P.J.: Scalar and pseudoscalar bifurcations: pattern formation in the visual cortex. Nonlinearity 14, 739\u2013775 (2001)","journal-title":"Nonlinearity"},{"issue":"4","key":"1512_CR8","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1007\/s002850000073","volume":"42","author":"P-L Buono","year":"2001","unstructured":"Buono, P.-L.: Models of central pattern generators for quadruped locomotion: II. Secondary gaits. J. Math. Biol. 42(4), 327\u2013346 (2001)","journal-title":"J. Math. Biol."},{"issue":"4","key":"1512_CR9","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1007\/s002850000058","volume":"42","author":"P-L Buono","year":"2001","unstructured":"Buono, P.-L., Golubitsky, M.: Models of central pattern generators for quadruped locomotion: I. Primary gaits. J. Math. Biol. 42(4), 291\u2013326 (2001)","journal-title":"J. Math. Biol."},{"key":"1512_CR10","first-page":"1","volume-title":"Nonlinear Phenomena in Physical and Biological Sciences","author":"J Cohen","year":"2000","unstructured":"Cohen, J., Stewart, I.: Polymorphism viewed as phenotypic symmetry-breaking. In: Malik, S.K. (ed.) Nonlinear Phenomena in Physical and Biological Sciences, pp. 1\u201367. Indian National Science Academy, New Delhi (2000)"},{"key":"1512_CR11","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/BF02429870","volume":"3","author":"JJ Collins","year":"1993","unstructured":"Collins, J.J., Stewart, I.: Coupled nonlinear oscillators and the symmetries of animal gaits. J. Nonlinear Sci. 3, 349\u2013392 (1993)","journal-title":"J. Nonlinear Sci."},{"key":"1512_CR12","doi-asserted-by":"crossref","first-page":"1465","DOI":"10.1142\/S0218127499001024","volume":"9","author":"G Chen","year":"1999","unstructured":"Chen, G., Ueta, T.: Yet another chaotic attractor. Int. J. Bifurcation Chaos 9, 1465\u20131466 (1999)","journal-title":"Int. J. Bifurcation Chaos"},{"key":"1512_CR13","unstructured":"Ermentrout, B.: XPPAUT $$\\textregistered $$ \u00ae \u2014the differential equations tool, version 5.98. http:\/\/www.math.pitt.edu\/bard\/xpp\/xpp.html (2006)"},{"issue":"2","key":"1512_CR14","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1137\/090756582","volume":"9","author":"N Filipski","year":"2010","unstructured":"Filipski, N., Golubitsky, M.: The Abelian Hopf $$H$$ H mod $$K$$ K theorem. SIAM J. Appl. Dyn. Syst. 9(2), 283\u2013291 (2010)","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"1512_CR15","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/s00332-003-0593-6","volume":"14","author":"M Golubitsky","year":"2004","unstructured":"Golubitsky, M., Nicol, M., Stewart, I.: Some curious phenomena in coupled cell systems. J. Nonlinear Sci. 14, 207\u2013236 (2004)","journal-title":"J. Nonlinear Sci."},{"key":"1512_CR16","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1090\/S0273-0979-06-01108-6","volume":"43","author":"M Golubitsky","year":"2006","unstructured":"Golubitsky, M., Stewart, I.: Nonlinear dynamics of networks: the groupoid formalism. Bull. Am. Math. Soc. 43, 305\u2013364 (2006)","journal-title":"Bull. Am. Math. Soc."},{"key":"1512_CR17","series-title":"Progress in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0348-8167-8","volume-title":"The Symmetry Perspective: From Equilibrium to Chaos in Phase Space and Physical Space","author":"M Golubitsky","year":"2002","unstructured":"Golubitsky, M., Stewart, I.: The Symmetry Perspective: From Equilibrium to Chaos in Phase Space and Physical Space. Progress in Mathematics, vol. 200. Birkh\u00e4user, Basel (2002)"},{"issue":"1","key":"1512_CR18","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1137\/040612634","volume":"4","author":"M Golubitsky","year":"2005","unstructured":"Golubitsky, M., Stewart, I., T\u00f6r\u00f6k, A.: Patterns of synchrony in coupled cell networks with multiple arrows. SIAM J. Appl. Dyn. Syst. 4(1), 78\u2013100 (2005)","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"1512_CR19","doi-asserted-by":"crossref","unstructured":"Golubitsky, M., Stewart, I., Schaeffer, D.G.: Singularities and Groups in Bifurcation Theory, vol. 2. Applied Mathematical Sciences 69. Springer-Verlag, New York (1988)","DOI":"10.1007\/978-1-4612-4574-2"},{"key":"1512_CR20","doi-asserted-by":"crossref","first-page":"023126","DOI":"10.1063\/1.4810932","volume":"23","author":"H Gu","year":"2013","unstructured":"Gu, H.: Experimental observation of transition from chaotic bursting to chaotic spiking in a neural pacemaker. Chaos 23, 023126 (2013)","journal-title":"Chaos"},{"key":"1512_CR21","doi-asserted-by":"crossref","unstructured":"Jiang, B., Han, X., Bi, Q.: Hopf bifurcation analysis in the T system. Nonlinear Anal. 11, 522\u2013527 (2010)","DOI":"10.1016\/j.nonrwa.2009.01.007"},{"key":"1512_CR22","unstructured":"Krupa, M., Szmolyan, P.: Relaxation oscillations and canard explosion. J. Differ. Equ. 174, 312\u2013368 (2001)"},{"key":"1512_CR23","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-69689-3","volume-title":"Chemical Oscillations, Waves, and Turbulence","author":"Y Kuramoto","year":"1984","unstructured":"Kuramoto, Y.: Chemical Oscillations, Waves, and Turbulence. Springer, Berlin (1984)"},{"key":"1512_CR24","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1016\/j.bulm.2003.09.006","volume":"66","author":"IS Labouriau","year":"2004","unstructured":"Labouriau, I.S., Alves-Pinto, C.M.: Loss of synchronization in partially coupled Hodgkin\u2013Huxley equations. Bull. Math. Biol. 66, 539\u2013557 (2004)","journal-title":"Bull. Math. Biol."},{"key":"1512_CR25","doi-asserted-by":"crossref","first-page":"2257","DOI":"10.1142\/S0218127402005819","volume":"12","author":"JH L\u00fc","year":"2002","unstructured":"L\u00fc, J.H., Zhou, T.S., Chen, G.R., Zhang, S.C.: Local bifurcation of the Chen system. Int. J. Bifurcation Chaos 12, 2257\u20132270 (2002)","journal-title":"Int. J. Bifurcation Chaos"},{"key":"1512_CR26","doi-asserted-by":"crossref","first-page":"043122","DOI":"10.1063\/1.4833115","volume":"23","author":"RM Nguimdo","year":"2013","unstructured":"Nguimdo, R.M., Tchitnga, R., Woafo, P.: Dynamics of coupled simplest chaotic two-component electronic circuits and its potential application to random bit generation. Chaos 23, 043122 (2013)","journal-title":"Chaos"},{"key":"1512_CR27","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1103\/PhysRevLett.64.821","volume":"64","author":"LM Pecora","year":"1990","unstructured":"Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821\u2013824 (1990)","journal-title":"Phys. Rev. Lett."},{"key":"1512_CR28","doi-asserted-by":"crossref","first-page":"2089","DOI":"10.1007\/s11071-012-0600-2","volume":"70","author":"CMA Pinto","year":"2012","unstructured":"Pinto, C.M.A.: Stability of quadruped robots\u2019 trajectories subjected to discrete perturbations. Nonlinear Dyn. 70, 2089\u20132094 (2012)","journal-title":"Nonlinear Dyn."},{"issue":"3","key":"1512_CR29","doi-asserted-by":"crossref","first-page":"1250064","DOI":"10.1142\/S0218127412500642","volume":"22","author":"CMA Pinto","year":"2012","unstructured":"Pinto, C.M.A.: Exotic dynamics in networks of coupled rings of cells. Int. J. Bifurcation Chaos 22(3), 1250064 (2012)","journal-title":"Int. J. Bifurcation Chaos"},{"issue":"3","key":"1512_CR30","doi-asserted-by":"crossref","first-page":"474","DOI":"10.1007\/s00285-006-0021-2","volume":"53","author":"CMA Pinto","year":"2006","unstructured":"Pinto, C.M.A., Golubitsky, M.: Central pattern generators for bipedal locomotion. J. Math. Biol. 53(3), 474\u2013489 (2006)","journal-title":"J. Math. Biol."},{"key":"1512_CR31","doi-asserted-by":"crossref","unstructured":"Santos, C.P., Matos, V., Pinto, C.M.A.: A Brainstem-like modulation approach for gait transition in a quadruped robot. In: Proceeding of the 2009 IEEE\/RSJ International Conference on Intelligent RObots and Systems, IROS 2009 (2009)","DOI":"10.1109\/IROS.2009.5354318"},{"issue":"4","key":"1512_CR32","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1137\/S1111111103419896","volume":"2","author":"I Stewart","year":"2003","unstructured":"Stewart, I., Golubitsky, M., Pivato, M.: Symmetry groupoids and patterns of synchrony in coupled cell networks. SIAM J. Appl. Dyn. Syst. 2(4), 609\u2013646 (2003)","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"1512_CR33","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1006\/jdeq.2001.4001","volume":"177","author":"P Szmolyan","year":"2001","unstructured":"Szmolyan, P., Wechselberger, M.: Canards in $${\\mathbf{R}}^3$$ R 3 . J. Differ. Equ. 177, 419\u2013453 (2001)","journal-title":"J. Differ. Equ."},{"key":"1512_CR34","unstructured":"The MathWorks, Inc. MATLAB $$\\textregistered $$ \u00ae , 1994\u20132012. http:\/\/www.mathworks.com"}],"container-title":["Nonlinear Dynamics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11071-014-1512-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11071-014-1512-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11071-014-1512-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,11]],"date-time":"2019-08-11T22:30:09Z","timestamp":1565562609000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11071-014-1512-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,6,26]]},"references-count":34,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2014,10]]}},"alternative-id":["1512"],"URL":"https:\/\/doi.org\/10.1007\/s11071-014-1512-0","relation":{},"ISSN":["0924-090X","1573-269X"],"issn-type":[{"value":"0924-090X","type":"print"},{"value":"1573-269X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,6,26]]}}}