{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T22:53:11Z","timestamp":1648680791547},"reference-count":10,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2003,4]]},"abstract":"<jats:p>Dissipative continuous dynamical systems with multiple external inputs are studied. When inputs are stochastically switched, the dynamics is characterized by trajectories with attractive fractal-like structures. We call this dynamics the fractal transition. This paper shows that a set of attractors obtained by periodic inputs can approximate trajectories of the fractal transition that have equal switching probabilities. The Hausdorff distance D is used to estimate the accuracy of approximation. We also present two numerical experiments, using harmonic and Duffing oscillators, corresponding to linear and nonlinear systems, respectively. We numerically show that D \u2243 0 given a large enough number of periodic inputs. For linear systems, under some conditions, we analytically derive the upper bound of D and show that D converges to 0.<\/jats:p>","DOI":"10.1142\/s0218127403007059","type":"journal-article","created":{"date-parts":[[2003,6,17]],"date-time":"2003-06-17T12:04:14Z","timestamp":1055851454000},"page":"943-950","source":"Crossref","is-referenced-by-count":2,"title":["APPROXIMATION OF THE FRACTAL TRANSITION USING ATTRACTORS EXCITED BY PERIODIC INPUTS"],"prefix":"10.1142","volume":"13","author":[{"given":"HISAKI","family":"OKA","sequence":"first","affiliation":[{"name":"Department of Applied Physics, Faculty of Engineering, Hokkaido University, Sapporo 060-8628, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"KAZUTOSHI","family":"GOHARA","sequence":"additional","affiliation":[{"name":"Department of Applied Physics, Faculty of Engineering, Hokkaido University, Sapporo 060-8628, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","volume-title":"Fractals Everywhere","author":"Barnsley M. F.","year":"1993"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218348X99000220"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1142\/S0218348X99000311"},{"key":"rf4","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1142\/S0218348X00000081","volume":"8","author":"Gohara K.","journal-title":"Fractals"},{"key":"rf5","volume-title":"Encounters with Chaos","author":"Gulick D.","year":"1992"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127402004772"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127401002158"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127401002602"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127401003395"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-9457(00)00018-X"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127403007059","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,3,21]],"date-time":"2020-03-21T21:09:53Z","timestamp":1584824993000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127403007059"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,4]]},"references-count":10,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2003,4]]}},"alternative-id":["10.1142\/S0218127403007059"],"URL":"https:\/\/doi.org\/10.1142\/s0218127403007059","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,4]]}}}