{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T14:32:44Z","timestamp":1787236364840,"version":"build-2736575974"},"reference-count":25,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Dyn. Syst."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>We study a novel phenomenon for coupled identical bursters: synchronized bursts where there are changes of spike synchrony within each burst. The examples we study are for normal form elliptic bursters where there is a periodic slow passage around a Bautin (codimension two degenerate Andronov\u2013Hopf) bifurcation. This burster has a subcritical Andronov\u2013Hopf bifurcation at the onset of repetitive spiking, while the end of burst occurs via a fold limit cycle bifurcation. We study synchronization behavior of two and three Bautin-type elliptic bursters for a linear direct coupling scheme as well as demonstrating the phenomenon in an approximation of gap-junction and synaptic coupling. Burst synchronization is known to be prevalent among such coupled bursters, while spike synchronization is more dependent on the details of the coupling. We note that higher order terms in the normal form that do not affect the behavior of a single burster can be responsible for changes in the synchrony pattern; more precisely, we find within-burst synchrony changes associated with a turning point in the spiking frequency.<\/jats:p>","DOI":"10.1137\/090746045","type":"journal-article","created":{"date-parts":[[2010,3,24]],"date-time":"2010-03-24T18:10:36Z","timestamp":1269454236000},"page":"261-281","source":"Crossref","is-referenced-by-count":11,"title":["Within-Burst Synchrony Changes for Coupled Elliptic Bursters"],"prefix":"10.1137","volume":"9","author":[{"given":"Abul Kalam al","family":"Azad","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter","family":"Ashwin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,3,24]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"P. Ashwin and J. Borresen,\n                      Encoding via conjugate symmetries of slow oscillations for globally coupled oscillators\n                      , Phys. Rev. E (3), 70 (2004), paper 026203.","DOI":"10.1103\/PhysRevE.70.026203"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1080\/14689360500151813"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/0149003"},{"key":"R4","doi-asserted-by":"crossref","unstructured":"S. Coombes and P. C. Bressloff, eds.\n                      Bursting, The Genesis of Rhythm in the Nervous System\n                      , World Scientific Publishing, Hackensack, NJ, 2005.","DOI":"10.1142\/5944"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/S0006-3495(93)81190-1"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/S0006-3495(93)81297-9"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139902412617"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"B. Ermentrout,\n                      Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students\n                      , Software Environ. Tools 14, SIAM, Philadelphia, 2002.","DOI":"10.1137\/1.9780898718195"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1137\/0146017"},{"key":"R10","doi-asserted-by":"crossref","unstructured":"M. Golubitsky, K. Josi\u0107, and L. Shiau,\n                      Bursting in coupled cell systems\n                      , in Bursting, The Genesis of Rhythm in the Nervous System, World Scientific Publishing, Hackensack, NJ, 2005, pp. 201\u2013221.","DOI":"10.1142\/9789812703231_0008"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127400000840"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144500382064"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1016\/S0303-2647(02)00067-9"},{"key":"R14","doi-asserted-by":"crossref","unstructured":"E. M. Izhikevich,\n                      Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting\n                      , MIT Press, Cambridge, MA, 2007.","DOI":"10.7551\/mitpress\/2526.001.0001"},{"key":"R15","unstructured":"Y. A. Kuznetsov,\n                      Elements of Applied Bifurcation Theory\n                      , 3rd ed., Appl. Math. Sci. 112, Springer-Verlag, New York, 2004."},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1016\/S0006-3495(98)77504-6"},{"key":"R17","first-page":"1385","volume":"23","author":"Neishtadt A. I.","year":"1987","journal-title":"Differential Equations","ISSN":"https:\/\/id.crossref.org\/issn\/0012-2661","issn-type":"print"},{"key":"R18","first-page":"171","volume":"24","author":"Neishtadt A. I.","year":"1988","journal-title":"Differential Equations","ISSN":"https:\/\/id.crossref.org\/issn\/0012-2661","issn-type":"print"},{"key":"R19","doi-asserted-by":"crossref","first-page":"1465","DOI":"10.1152\/jn.1999.82.3.1465","volume":"82","author":"Pedroarena C. M.","year":"1999","journal-title":"Neurophysiol.","ISSN":"https:\/\/id.crossref.org\/issn\/0090-2977","issn-type":"print"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.78.1213"},{"key":"R21","doi-asserted-by":"crossref","unstructured":"J. Rinzel,\n                      A formal classification of bursting mechanisms in excitable systems\n                      , in Mathematical Topics in Population Biology, Morphogenesis and Neurosciences (Kyoto, 1985), Lecture Notes in Biomath. 71, Springer, Berlin, 1987, pp. 267\u2013281.","DOI":"10.1007\/978-3-642-93360-8_26"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1007\/BF00275501"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1080\/14689360117083"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1007\/BF02458269"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/17\/1\/009"}],"container-title":["SIAM Journal on Applied Dynamical Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/090746045","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:28:28Z","timestamp":1787232508000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/090746045"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":25,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/090746045"],"URL":"https:\/\/doi.org\/10.1137\/090746045","relation":{},"ISSN":["1536-0040"],"issn-type":[{"value":"1536-0040","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}