{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T16:58:49Z","timestamp":1649091529019},"reference-count":34,"publisher":"World Scientific Pub Co Pte Lt","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2004,11]]},"abstract":"<jats:p> We consider a bifurcation that occurs in some two-dimensional vector fields, namely a codimension-one bifurcation in which there is simultaneously the creation of a pair of equilibria via a steady state bifurcation and the destruction of a large amplitude periodic orbit. We show that this phenomenon may occur in an unfolding of the saddle-node\/pitchfork normal form equations, although not near the saddle-node\/pitchfork instability. By construction and analysis of a return map, we show that the codimension-one bifurcation emerges from a codimension-two point at which there is a heteroclinic bifurcation between two saddle equilibria, one hyperbolic and the other nonhyperbolic. We find the same phenomenon occurs in the normal form equations for the hysteresis\/pitchfork bifurcation, in this case arbitrarily close to the instability, and show there are restrictions regarding the way in which such dynamics can occur near pitchfork\/pitchfork bifurcations. These conclusions carry over to analogous phenomena in normal forms for steady state\/Hopf bifurcations. <\/jats:p>","DOI":"10.1142\/s0218127404011752","type":"journal-article","created":{"date-parts":[[2005,3,11]],"date-time":"2005-03-11T06:52:56Z","timestamp":1110523976000},"page":"3855-3869","source":"Crossref","is-referenced-by-count":1,"title":["A REMARK ON HETEROCLINIC BIFURCATIONS NEAR STEADY STATE\/PITCHFORK BIFURCATIONS"],"prefix":"10.1142","volume":"14","author":[{"given":"VIVIEN","family":"KIRK","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"EDGAR","family":"KNOBLOCH","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/12\/4\/324"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127499000936"},{"key":"rf3","first-page":"016303","volume":"65","author":"Batiste O.","journal-title":"Phys. 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