{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T09:27:49Z","timestamp":1775122069258,"version":"3.50.1"},"reference-count":37,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2014,8]]},"abstract":"<jats:p> We study the synchronization of bursting cells that are coupled through both excitatory and inhibitory connections. We extend our recent results on networks of Hindmarsh\u2013Rose bursting neurons [Belykh et al., 2014] to coupled Sherman \u03b2-cell models and show that the addition of repulsive inhibition to an excitatory network can induce synchronization. We discuss the mechanism of this purely synergenic phenomenon and demonstrate that the inhibition leads to the disappearance of a homoclinic bifurcation that governs the type of synchronized bursting. As a result, the inhibition causes the transition from square-wave to easier-to-synchronize plateau bursting, so that weaker excitation is sufficient to induce bursting synchrony. We dedicate this paper to the memory of Leonid P. Shilnikov, the pioneer of homoclinic bifurcation theory, and emphasize the importance of homoclinic bifurcations for understanding the emergence of synchronized rhythms in bursting networks. <\/jats:p>","DOI":"10.1142\/s0218127414400136","type":"journal-article","created":{"date-parts":[[2014,8,29]],"date-time":"2014-08-29T08:35:53Z","timestamp":1409301353000},"page":"1440013","source":"Crossref","is-referenced-by-count":12,"title":["When Transitions Between Bursting Modes Induce Neural Synchrony"],"prefix":"10.1142","volume":"24","author":[{"given":"Reimbay","family":"Reimbayev","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics and Neuroscience Institute, Georgia State University, 30 Pryor Street, Atlanta, GA 30303, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Igor","family":"Belykh","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics and Neuroscience Institute, Georgia State University, 30 Pryor Street, Atlanta, GA 30303, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2014,8,29]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/s101890070012"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.94.188101"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.101.078102"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1063\/1.3563581"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/BF02460633"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/s004220050507"},{"key":"rf8","doi-asserted-by":"crossref","first-page":"1166","DOI":"10.1152\/jn.2002.88.3.1166","volume":"88","author":"Elson R. C.","year":"2002","journal-title":"J. Neurophysiol."},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.74.031922"},{"key":"rf10","unstructured":"M.\u00a0Golubitsky, K.\u00a0Josic and T.\u00a0Kaper, Festschrift Dedicated to Floris Takens, Global Analysis of Dynamical Systems (2001)\u00a0pp. 277\u2013308."},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1137\/S1111111101394040"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1098\/rspb.1984.0024"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127400000840"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144500382064"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.85.036214"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1016\/S1874-575X(02)80022-4"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0406343101"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-93360-8_26"},{"key":"rf19","unstructured":"J.\u00a0Rinzel and B.\u00a0Ermentrout, Methods in Neuronal Modeling, eds. C.\u00a0Koch and I.\u00a0Segev (MIT Press, Cambridge, MA, 1989)\u00a0pp. 251\u2013291."},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1137\/S111111110240323X"},{"key":"rf21","first-page":"811","volume":"56","author":"Sherman A.","year":"1994","journal-title":"Bull. Math. Biol."},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1142\/9789812798596"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1142\/9789812798558"},{"key":"rf24","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.71.056214"},{"key":"rf25","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.94.048101"},{"key":"rf26","doi-asserted-by":"publisher","DOI":"10.1063\/1.2959850"},{"key":"rf27","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127408021634"},{"key":"rf28","doi-asserted-by":"publisher","DOI":"10.1007\/s11538-007-9241-x"},{"key":"rf29","doi-asserted-by":"publisher","DOI":"10.1007\/BF00198772"},{"key":"rf30","doi-asserted-by":"publisher","DOI":"10.1137\/0151071"},{"key":"rf31","doi-asserted-by":"publisher","DOI":"10.1007\/BF02429854"},{"key":"rf32","first-page":"596","volume":"342","author":"Turaev D. V.","year":"1995","journal-title":"Soviet Math. Dokl."},{"key":"rf33","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2010.03.030"},{"key":"rf34","doi-asserted-by":"publisher","DOI":"10.1007\/BF00961879"},{"key":"rf35","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1992.4.1.84"},{"key":"rf36","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(93)90286-A"},{"key":"rf37","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.83.056209"},{"key":"rf38","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0092918"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127414400136","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T20:32:32Z","timestamp":1565123552000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127414400136"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,8]]},"references-count":37,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2014,8,29]]},"published-print":{"date-parts":[[2014,8]]}},"alternative-id":["10.1142\/S0218127414400136"],"URL":"https:\/\/doi.org\/10.1142\/s0218127414400136","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,8]]}}}