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This paper gives a brief historical review of the development of stability analysis in these systems, induced by newer and newer models in several fields of engineering. Local and global nonlinear behavior is also discussed in the case of the most typical parametrically excited delayed oscillator, a recent model of cutting applied to the study of high-speed milling processes.<\/jats:p>","DOI":"10.1142\/s0218127405013642","type":"journal-article","created":{"date-parts":[[2005,10,26]],"date-time":"2005-10-26T11:55:00Z","timestamp":1130327700000},"page":"2783-2798","source":"Crossref","is-referenced-by-count":96,"title":["DELAY, PARAMETRIC EXCITATION, AND THE NONLINEAR DYNAMICS OF CUTTING PROCESSES"],"prefix":"10.1142","volume":"15","author":[{"given":"G\u00c1BOR","family":"ST\u00c9P\u00c1N","sequence":"first","affiliation":[{"name":"Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, H-1521, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"TAM\u00c1S","family":"INSPERGER","sequence":"additional","affiliation":[{"name":"Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, H-1521, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R\u00d3BERT","family":"SZALAI","sequence":"additional","affiliation":[{"name":"Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, H-1521, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/S0007-8506(07)62342-7"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2000.0755"},{"key":"rf4","volume-title":"Differential-Difference Equations","author":"Bellman R.","year":"1963"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1115\/1.3624967"},{"key":"rf6","first-page":"65","volume":"21","author":"Campbell S. 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