{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,22]],"date-time":"2024-06-22T07:53:27Z","timestamp":1719042807394},"reference-count":28,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2005,6]]},"abstract":"<jats:p> In this paper, a special nonsmooth transformation of time is combined with the shooting algorithm for visualization of the manifolds of periodic solutions and their bifurcations. The general class of nonlinear oscillators under smooth, nonsmooth, and impulsive loadings is considered. The corresponding boundary value problems with no singularities are obtained by introducing the periodic piecewise-linear (sawtooth) temporal argument. The Ueda circuit, that is Duffing's oscillator with no linear stiffness, is considered for illustration. It is shown that the temporal mode shape of the input can be responsible for qualitative features of the dynamics, such as transitions between the regular and random motions. The important role of unstable periodic orbits and their links with strange attractors are discussed. <\/jats:p>","DOI":"10.1142\/s0218127405013034","type":"journal-article","created":{"date-parts":[[2005,8,17]],"date-time":"2005-08-17T01:25:54Z","timestamp":1124241954000},"page":"1879-1899","source":"Crossref","is-referenced-by-count":20,"title":["TEMPORAL TRANSFORMATIONS AND VISUALIZATION DIAGRAMS FOR NONSMOOTH PERIODIC MOTIONS"],"prefix":"10.1142","volume":"15","author":[{"given":"V. N.","family":"PILIPCHUK","sequence":"first","affiliation":[{"name":"Wayne State University, College of Engineering, Detroit, MI 48202, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971231"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.58.2387"},{"key":"rf3","volume-title":"Nonlinearity, Bifurcation and Chaos: The Doors to the Future","author":"Awrejcewicz J.","year":"1999"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127402004668"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1142\/9789812564801"},{"key":"rf6","volume-title":"Mathematica for Scientists and Engineers","author":"Bahler T. B.","year":"1995"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-7793-9"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1115\/1.1345524"},{"key":"rf9","doi-asserted-by":"crossref","first-page":"1711","DOI":"10.1103\/PhysRevA.37.1711","volume":"37","author":"Grebogi C.","journal-title":"Phys. Rev."},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827599359278"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-50085-5"},{"key":"rf12","volume-title":"Metod Normalnykh Kolebanii dlya Sushchestvenno Nelineinykh Sistem","author":"Manevich L. I.","year":"1989"},{"key":"rf13","first-page":"63","volume":"36","author":"Maslov V. P.","journal-title":"Uspekhi Mat. Nauk"},{"key":"rf14","volume-title":"Introduction to Non-linear Mechanics","author":"Minorsky N.","year":"1947"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.64.1196"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-3486-9"},{"key":"rf17","first-page":"37","author":"Pilipchuk V. N.","journal-title":"Dokl. Akad. Nauk Ukrain. SSR"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1006\/jsvi.1996.0175"},{"key":"rf19","first-page":"145","volume":"100","author":"Pilipchuk V. N.","journal-title":"Physica"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008331427364"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1016\/S0960-0779(01)00245-4"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-46378-5"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008354208466"},{"key":"rf24","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-7462(01)00144-5"},{"key":"rf25","volume-title":"Green's Functions and Boundary Value Problems","author":"Stakgold I.","year":"1979"},{"key":"rf26","doi-asserted-by":"publisher","DOI":"10.1007\/BF01011512"},{"key":"rf27","doi-asserted-by":"publisher","DOI":"10.1002\/9783527617869"},{"key":"rf28","doi-asserted-by":"publisher","DOI":"10.1142\/3345"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127405013034","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T15:01:31Z","timestamp":1565190091000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127405013034"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,6]]},"references-count":28,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2005,6]]}},"alternative-id":["10.1142\/S0218127405013034"],"URL":"https:\/\/doi.org\/10.1142\/s0218127405013034","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,6]]}}}