{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T01:44:36Z","timestamp":1778031876467,"version":"3.51.4"},"reference-count":19,"publisher":"World Scientific Pub Co Pte Lt","issue":"12","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2013,12]]},"abstract":"<jats:p> Based on the detailed bifurcation analysis and the master stability function, bursting types and stable domains of the parameter space of the Rulkov map-based neuron network coupled by the mean field are taken into account. One of our main findings is that besides the square-wave bursting, there at least exist two kinds of triangle burstings after the mean field coupling, which can be determined by the crisis bifurcation, the flip bifurcation, and the saddle-node bifurcation. Under certain coupling conditions, there exists two kinds of striking transitions from the square-wave bursting (the spiking) to the triangle bursting (the square-wave bursting). Stable domains of fixed points, periodic solutions, quasiperiodic solutions and their corresponding firing regimes in the parameter space are presented in a rigorous mathematical way. In particular, as a function of the intrinsic control parameters of each single neuron and the external coupling strength, a stable coefficient of the Neimark\u2013Sacker bifurcation is derived in a parameter plane. These results show that there exist complex dynamics and rich firing regimes in such a simple but thought-provoking neuron network. <\/jats:p>","DOI":"10.1142\/s0218127413300413","type":"journal-article","created":{"date-parts":[[2014,1,7]],"date-time":"2014-01-07T07:29:22Z","timestamp":1389079762000},"page":"1330041","source":"Crossref","is-referenced-by-count":19,"title":["BURSTING TYPES AND STABLE DOMAINS OF RULKOV NEURON NETWORK WITH MEAN FIELD COUPLING"],"prefix":"10.1142","volume":"23","author":[{"given":"HONGJUN","family":"CAO","sequence":"first","affiliation":[{"name":"Department of Mathematics, School of Science, Beijing Jiaotong University, Shang Yuan Cun 3, Haidian District, Beijing 100044, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"YANGUO","family":"WU","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Nanyang Normal University, Nanyang 473061, P. R. 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