{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,5,18]],"date-time":"2022-05-18T05:41:53Z","timestamp":1652852513038},"reference-count":14,"publisher":"World Scientific Pub Co Pte Ltd","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2015,6,30]]},"abstract":"<jats:p>We consider a general uncertain nonlinear dynamical system defined in a certain model set, and reformulate a problem of robustness bifurcation analysis (RBA), which has been originally formulated in our previous work. As such, we develop an efficient computational method for the RBA, which can be used for quantitative evaluation of bifurcation robustness in uncertain dynamical systems. Specifically, we first linearize the uncertain system properly and then apply a feedback transformation technique to reduce the RBA problem to a linear robustness analysis one, which can be solved using \u03bc-analysis, a common analysis technique in robust control theory. Finally, we provide robustness analysis of a gene regulatory network model where oscillatory behavior appears according to Hopf bifurcation. We give quantitative evaluation of the bifurcation robustness using the RBA method proposed here.<\/jats:p>","DOI":"10.1142\/s021812741540012x","type":"journal-article","created":{"date-parts":[[2015,7,16]],"date-time":"2015-07-16T11:23:03Z","timestamp":1437045783000},"page":"1540012","source":"Crossref","is-referenced-by-count":0,"title":["A Computational Method for Robust Bifurcation Analysis and Its Application to Biomolecular Systems"],"prefix":"10.1142","volume":"25","author":[{"given":"Masaki","family":"Inoue","sequence":"first","affiliation":[{"name":"Faculty of Science and Technology, Keio University, 3-14-1, Hiyoshi, Kohoku-ku, Yokohama, Kanagawa 223-8522, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hikaru","family":"Ikuta","sequence":"additional","affiliation":[{"name":"Faculty of Science and Technology, Keio University, 3-14-1, Hiyoshi, Kohoku-ku, Yokohama, Kanagawa 223-8522, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuichi","family":"Adachi","sequence":"additional","affiliation":[{"name":"Faculty of Science and Technology, Keio University, 3-14-1, Hiyoshi, Kohoku-ku, Yokohama, Kanagawa 223-8522, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun-Ichi","family":"Imura","sequence":"additional","affiliation":[{"name":"Graduate School of Information Science and Engineering, Tokyo Institute of Technology, 2-12-1-W8-1, O-okayama, Meguro-ku, Tokyo 152-8552, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kazuyuki","family":"Aihara","sequence":"additional","affiliation":[{"name":"Institute of Industrial Science, the University of Tokyo, 4-6-1, Komaba, Meguro-ku, Tokyo 153-8505, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2015,7,16]]},"reference":[{"key":"rf1","doi-asserted-by":"crossref","DOI":"10.1201\/9781420011432","volume-title":"An Introduction to Systems Biology: Design Principles of Biological Circuits","author":"Alon U.","year":"2006"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/0005-1098(94)90164-3"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1109\/81.128018"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1109\/9.256397"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1049\/ip-d.1982.0053"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1038\/35002125"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1038\/35002131"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127413501575"},{"key":"rf13","doi-asserted-by":"crossref","DOI":"10.1201\/9781482227871","volume-title":"Dynamical Systems: Stability, Symbolic Dynamics, and Chaos","author":"Robinson C.","year":"1998"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3108-8"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1016\/j.cell.2013.05.001"},{"key":"rf16","volume-title":"Multivariable Feedback Control: Analysis and Design","author":"Skogestad S.","year":"2005"},{"key":"rf17","volume-title":"Introduction to Applied Nonlinear Dynamical Systems and Chaos","author":"Wiggins S.","year":"2003"},{"key":"rf18","volume-title":"Robust and Optimal Control","author":"Zhou K.","year":"1996"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021812741540012X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,18]],"date-time":"2022-05-18T05:26:34Z","timestamp":1652851594000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021812741540012X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,6,30]]},"references-count":14,"journal-issue":{"issue":"07","published-online":{"date-parts":[[2015,7,16]]},"published-print":{"date-parts":[[2015,6,30]]}},"alternative-id":["10.1142\/S021812741540012X"],"URL":"https:\/\/doi.org\/10.1142\/s021812741540012x","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,6,30]]}}}