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We present a series of models of increasing simplicity that capture the significant features of the network's behavior. Our simplest model is a piecewise linear, discontinuous one-dimensional map. This map helps explain the structure of the bifurcation diagram, and allows us to directly determine Lyapunov exponents, which give a measure of the system's predictability. As a result, we are able to more precisely describe and categorize the dynamics, including chaos, exhibited by this network.<\/jats:p>","DOI":"10.1142\/s0218127409024700","type":"journal-article","created":{"date-parts":[[2009,12,15]],"date-time":"2009-12-15T11:45:55Z","timestamp":1260877555000},"page":"3129-3141","source":"Crossref","is-referenced-by-count":1,"title":["BIFURCATIONS AND CHAOS IN A PERIODICALLY PROBED COMPUTER NETWORK"],"prefix":"10.1142","volume":"19","author":[{"given":"IAN","family":"FROMMER","sequence":"first","affiliation":[{"name":"US Coast Guard Academy, New London, CT 06320, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ERIC","family":"HARDER","sequence":"additional","affiliation":[{"name":"US Department of Defense, College Park, MD 20742, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"BRIAN","family":"HUNT","sequence":"additional","affiliation":[{"name":"University of Maryland, College Park, MD 20742, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"RYAN","family":"LANCE","sequence":"additional","affiliation":[{"name":"US Department of Defense, College Park, MD 20742, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"EDWARD","family":"OTT","sequence":"additional","affiliation":[{"name":"University of Maryland, College Park, MD 20742, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JAMES","family":"YORKE","sequence":"additional","affiliation":[{"name":"University of Maryland, College Park, MD 20742, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,5,2]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.1997.657890"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1145\/885651.781036"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(90)90119-9"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127495000302"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1080\/02681119608806224"},{"key":"p_6","first-page":"926","author":"Ebrahimi-Taghizadeh S.","year":"2005","journal-title":"Proc. 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