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Particular attention is focused on dynamics associated with the semisimple singularity, and both the MTS and CMR methods are applied to compute the normal forms near the semisimple singular point. For the ordinary differential equations (ODE), we show that the two methods are equivalent up to any order in computing the normal forms; while for the differential equations with delays, we obtain the conditions under which the normal forms, derived by using the MTS and CMR methods, are identical up to third order. Different types of practical examples with delays are presented to demonstrate the application of the theoretical results, associated with Hopf, Hopf-zero and double-Hopf singularities.<\/jats:p>","DOI":"10.1142\/s0218127414500035","type":"journal-article","created":{"date-parts":[[2014,2,20]],"date-time":"2014-02-20T06:27:33Z","timestamp":1392877653000},"page":"1450003","source":"Crossref","is-referenced-by-count":16,"title":["Equivalence of the MTS Method and CMR Method for Differential Equations Associated with Semisimple Singularity"],"prefix":"10.1142","volume":"24","author":[{"given":"Pei","family":"Yu","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Western University, London, Ontario, Canada N6A 5B7, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuting","family":"Ding","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Northeast Forestry University, Harbin 150040, P. R. 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