{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T22:11:03Z","timestamp":1779315063827,"version":"3.51.4"},"reference-count":20,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2010,6]]},"abstract":"<jats:p> The continuous Bonhoeffer\u2013van der Pol (BVP for short) oscillator is transformed into a map-based BVP model by using the forward Euler scheme. At first, the bifurcations and chaos of the map-based BVP model are investigated when the step size varies as a bifurcation parameter. By using the fast-slow decomposition technique, a two-parameter bifurcation diagram is obtained to give insight into the effect of the step size on bifurcations and chaos of the map-based BVP model. The investigation shows that the period-doubling bifurcation is dependent on the step size, while the saddle-node bifurcation is independent of the step size. Second, when the fast\u2013slow decomposition technique cannot be used, we rigorously prove that in the map-based BVP model there exists chaos in the sense of Marotto when the discrete step size varies as a bifurcation parameter. These results show that the discrete step sizes play a vital role between the continuous-time dynamical system and the corresponding discrete dynamical system. Much attention should be paid on the step size when a map-based neuron model is used as an alternative to a continuous neuron model. <\/jats:p>","DOI":"10.1142\/s0218127410026836","type":"journal-article","created":{"date-parts":[[2010,6,25]],"date-time":"2010-06-25T07:34:29Z","timestamp":1277451269000},"page":"1789-1795","source":"Crossref","is-referenced-by-count":4,"title":["EFFECT OF STEP SIZE ON BIFURCATIONS AND CHAOS OF A MAP-BASED BVP OSCILLATOR"],"prefix":"10.1142","volume":"20","author":[{"given":"HONGJUN","family":"CAO","sequence":"first","affiliation":[{"name":"Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"CAIXIA","family":"WANG","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"MIGUEL A. F.","family":"SANJU\u00c1N","sequence":"additional","affiliation":[{"name":"Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de F\u00edsica, Universidad Rey Juan Carlos, Tulip\u00e1n s\/n, 28933 M\u00f3stoles, Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,5,2]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/S0362-546X(01)00896-3"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/s10339-008-0222-2"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.91.208102"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1142\/S021798490400789X"},{"key":"rf5","first-page":"051914-1","volume":"64","author":"De Vries G.","journal-title":"Phys. Rev. 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