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Through an algebraic formulation for tree and cycle graphs, we provide upper bounds on this number using the theory of the birationally invariant intersection index of a family of rational functions. These bounds are significant and make asymptotic improvements over the best existing bound.<\/jats:p>","DOI":"10.1137\/17m1145665","type":"journal-article","created":{"date-parts":[[2018,10,23]],"date-time":"2018-10-23T13:45:02Z","timestamp":1540302302000},"page":"489-507","source":"Crossref","is-referenced-by-count":21,"title":["Counting Equilibria of the Kuramoto Model Using Birationally Invariant Intersection Index"],"prefix":"10.1137","volume":"2","author":[{"given":"Tianran","family":"Chen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robert","family":"Davis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dhagash","family":"Mehta","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,10,23]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.77.137"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1982.1085093"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2013.03.007"},{"key":"atypb4","doi-asserted-by":"crossref","unstructured":"M. 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