{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:39:02Z","timestamp":1772296742754,"version":"3.50.1"},"reference-count":36,"publisher":"World Scientific Pub Co Pte Lt","issue":"10","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2003,10]]},"abstract":"<jats:p> We present a numerical method for branch switching between homoclinic orbits to equilibria of ODEs computed via numerical continuation. Starting from a 1-homoclinic orbit our method allows us to find and follow an N-homoclinic orbit, for any N&gt;1 (if it exists nearby). This scheme is based on Lin's method and it is robust and reliable. <\/jats:p><jats:p> The method is implemented in AUTO\/HOMCONT. A system of ordinary differential equations introduced by Sandstede featuring inclination and orbit flip bifurcations and homoclinic-doubling cascades, is used as a test bed for the algorithm. It is also successfully applied to reliably find multihump traveling wave solutions in the FitzHugh\u2013Nagumo nerve-axon equations and in a fourth-order Hamiltonian system arising as a model for water waves. <\/jats:p>","DOI":"10.1142\/s0218127403008326","type":"journal-article","created":{"date-parts":[[2003,12,1]],"date-time":"2003-12-01T04:06:11Z","timestamp":1070251571000},"page":"2977-2999","source":"Crossref","is-referenced-by-count":32,"title":["HOMOCLINIC BRANCH SWITCHING: A NUMERICAL IMPLEMENTATION OF LIN'S METHOD"],"prefix":"10.1142","volume":"13","author":[{"given":"BART E.","family":"OLDEMAN","sequence":"first","affiliation":[{"name":"Department of Engineering Mathematics, University of Bristol, Bristol BS8 1TR, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ALAN R.","family":"CHAMPNEYS","sequence":"additional","affiliation":[{"name":"Department of Engineering Mathematics, University of Bristol, Bristol BS8 1TR, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"BERND","family":"KRAUSKOPF","sequence":"additional","affiliation":[{"name":"Department of Engineering Mathematics, University of Bristol, Bristol BS8 1TR, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","first-page":"219","volume":"9","author":"Belyakov L. 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