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Based on the generalized harmonic balance, the analytical solutions of periodic motions in nonlinear dynamical systems with\/without time-delay are reviewed, and the analytical solutions for period-m motion to quasi-periodic motion are discussed. The analytical bifurcation trees of period-1 motion to chaos are presented as an application. <\/jats:p>","DOI":"10.1142\/s0218127414300134","type":"journal-article","created":{"date-parts":[[2014,4,23]],"date-time":"2014-04-23T09:12:34Z","timestamp":1398244354000},"page":"1430013","source":"Crossref","is-referenced-by-count":22,"title":["On Analytical Routes to Chaos in Nonlinear Systems"],"prefix":"10.1142","volume":"24","author":[{"given":"Albert C. 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