{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,3]],"date-time":"2025-12-03T17:39:30Z","timestamp":1764783570721},"reference-count":16,"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> We consider the macroscopic, second order model of Kerner\u2013Konh\u00e4user for traffic flow given by a system of PDE. Assuming conservation of cars, traveling waves solution of the PDE are reduced to a dynamical system in the plane. We prove that under generic conditions on the so-called fundamental diagram, the surface of critical points has a fold or cusp catastrophe and each fold point gives rise to a Takens\u2013Bogdanov bifurcation. In particular, limit cycles arising from a Hopf bifurcation give place to traveling wave solutions of the PDE. <\/jats:p>","DOI":"10.1142\/s0218127413501915","type":"journal-article","created":{"date-parts":[[2014,1,7]],"date-time":"2014-01-07T07:29:22Z","timestamp":1389079762000},"page":"1350191","source":"Crossref","is-referenced-by-count":13,"title":["TRAVELING WAVES, CATASTROPHES AND BIFURCATIONS IN A GENERIC SECOND ORDER TRAFFIC FLOW MODEL"],"prefix":"10.1142","volume":"23","author":[{"given":"FRANCISCO A.","family":"CARRILLO","sequence":"first","affiliation":[{"name":"Mathematics Department, Universidad de Sonora, MEX. Blvd. Luis Encinas y Rosales S\/N, Col. Centro, Hermosillo, Sonora, M\u00e9xico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JOAQU\u00cdN","family":"DELGADO","sequence":"additional","affiliation":[{"name":"Mathematics Department, UAM\u2013Iztapalapa. 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