{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:28:44Z","timestamp":1747189724344,"version":"3.40.5"},"reference-count":14,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2021,3,30]]},"abstract":"<jats:p> In modern times, satellite-based global positioning and navigation systems, such as the GPS, include precise time-keeping devices, e.g. atomic clocks, which are crucial for navigation and for a wide range of economic and industrial applications. However, precise timing might not be available when the environment renders satellite equipment inoperable. In response to this critical need, we have been carrying out, over the past three years, theory and preliminary experiments [Buono et al., 2018a; Buono et al., 2018b; Palacios et al., 2020], towards developing a novel and inexpensive precision timing device that can function independently of GPS availability. The fundamental idea is to exploit collective behavior generated by networks of coupled nonlinear oscillators. Common sense may suggest that synchronized oscillations may lead to higher accuracy. Previous works show, however, that it is not synchronization but rather, traveling wave patterns, in which consecutive oscillators are out of phase by a constant amount, that can better reduce the negative effects of noise and material imperfections which cause phase drift. In this work we advance the state-of-art in the network-based concept by studying, mainly computationally, collective behavior in networks of Colpitts oscillators. These type of oscillators are chosen because they offer a wide range of advantages (such as the ability to tune up the oscillations over a broad frequency range). The results highlight the regions of parameter space, including coupling strength, where traveling wave patterns have the largest basins of attraction and the ability to reduce phase drift by a [Formula: see text] scaling law, where [Formula: see text] is the number of oscillators in the network. The results should also provide guidelines for follow-up design and fabrication tasks of a network-based technology for precision timing. <\/jats:p>","DOI":"10.1142\/s021812742130010x","type":"journal-article","created":{"date-parts":[[2021,4,1]],"date-time":"2021-04-01T09:17:12Z","timestamp":1617268632000},"page":"2130010","source":"Crossref","is-referenced-by-count":1,"title":["Phase Drift in Networks of Coupled Colpitts Oscillators"],"prefix":"10.1142","volume":"31","author":[{"given":"Lourdes","family":"Coria","sequence":"first","affiliation":[{"name":"Nonlinear Dynamical Systems Group, Department of Mathematics, San Diego State University, San Diego, CA 92182, USA"}]},{"given":"Horacio","family":"Lopez","sequence":"additional","affiliation":[{"name":"Nonlinear Dynamical Systems Group, Department of Mathematics, San Diego State University, San Diego, CA 92182, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0580-3657","authenticated-orcid":false,"given":"Antonio","family":"Palacios","sequence":"additional","affiliation":[{"name":"Nonlinear Dynamical Systems Group, Department of Mathematics, San Diego State University, San Diego, CA 92182, USA"}]},{"given":"Visarath","family":"In","sequence":"additional","affiliation":[{"name":"Naval Information Warfare Center Pacific, Code 71740, 53560 Hull Street, San Diego, CA 92152-5001, USA"}]},{"given":"Patrick","family":"Longhini","sequence":"additional","affiliation":[{"name":"Naval Information Warfare Center Pacific, Code 71740, 53560 Hull Street, San Diego, CA 92152-5001, USA"}]}],"member":"219","published-online":{"date-parts":[[2021,3,30]]},"reference":[{"key":"S021812742130010XBIB001","series-title":"Mathematics in Science and Engineering","volume-title":"Stochastic Systems","volume":"169","author":"Adomian G.","year":"1983"},{"key":"S021812742130010XBIB003","doi-asserted-by":"publisher","DOI":"10.1137\/16M1066154"},{"key":"S021812742130010XBIB004","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.98.012203"},{"key":"S021812742130010XBIB005","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127403008338"},{"volume-title":"Auto94: Software for Continuation and Bifurcation Problems in Ordinary Differential Equations","year":"1994","author":"Doedel E.","key":"S021812742130010XBIB006"},{"key":"S021812742130010XBIB007","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127400000670"},{"key":"S021812742130010XBIB008","series-title":"Springer Series in Synergetics","volume-title":"Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences","author":"Gardiner C.","year":"2003","edition":"3"},{"volume-title":"The Symmetry Perspective","year":"2000","author":"Golubitsky M.","key":"S021812742130010XBIB009"},{"volume-title":"An Exploration of Random Processes for Engineers","year":"2006","author":"Hajek B.","key":"S021812742130010XBIB010"},{"key":"S021812742130010XBIB011","doi-asserted-by":"publisher","DOI":"10.1109\/81.331536"},{"key":"S021812742130010XBIB012","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2004.832793"},{"key":"S021812742130010XBIB013","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127420502533"},{"key":"S021812742130010XBIB014","series-title":"Oxford Series in Electrical and Computer Engineering","volume-title":"Microelectronic Circuits","author":"Sedra A.","year":"1998"},{"key":"S021812742130010XBIB015","doi-asserted-by":"publisher","DOI":"10.1142\/8328"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021812742130010X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,1]],"date-time":"2021-04-01T09:18:58Z","timestamp":1617268738000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021812742130010X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,30]]},"references-count":14,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2021,3,30]]}},"alternative-id":["10.1142\/S021812742130010X"],"URL":"https:\/\/doi.org\/10.1142\/s021812742130010x","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"type":"print","value":"0218-1274"},{"type":"electronic","value":"1793-6551"}],"subject":[],"published":{"date-parts":[[2021,3,30]]}}}