{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:41:52Z","timestamp":1740134512492,"version":"3.37.3"},"reference-count":16,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11171053","11001040"],"award-info":[{"award-number":["11171053","11001040"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of China Youth Fund","award":["11171053","11001040"],"award-info":[{"award-number":["11171053","11001040"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>We propose an approach for constructing Lyapunov function in quadratic form of a differential system. First, positive polynomial system is obtained via the local property of the Lyapunov function as well as its derivative. Then, the positive polynomial system is converted into an equation system by adding some variables. Finally, numerical technique is applied to solve the equation system. Some experiments show the efficiency of our new algorithm.<\/jats:p>","DOI":"10.1155\/2013\/859578","type":"journal-article","created":{"date-parts":[[2013,12,18]],"date-time":"2013-12-18T17:01:06Z","timestamp":1387386066000},"page":"1-5","source":"Crossref","is-referenced-by-count":6,"title":["Constructing the Lyapunov Function through Solving Positive Dimensional Polynomial System"],"prefix":"10.1155","volume":"2013","author":[{"given":"Zhenyi","family":"Ji","sequence":"first","affiliation":[{"name":"Laboratory of Computer Reasoning and Trustworthy Computation, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"},{"name":"Laboratory of Automated Reasoning and Cognition, Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Science, Chongqing 401120, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1169-379X","authenticated-orcid":true,"given":"Wenyuan","family":"Wu","sequence":"additional","affiliation":[{"name":"Laboratory of Automated Reasoning and Cognition, Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Science, Chongqing 401120, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yong","family":"Feng","sequence":"additional","affiliation":[{"name":"Laboratory of Automated Reasoning and Cognition, Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Science, Chongqing 401120, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guofeng","family":"Zhang","sequence":"additional","affiliation":[{"name":"L.A.S Department of ChengDu College, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"issue":"3","key":"1","doi-asserted-by":"crossref","first-page":"241","DOI":"10.9746\/sicetr1965.42.241","volume":"42","year":"2006","journal-title":"Transactions of the Society of Instrument and Control Engineers"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1093\/ietfec\/e89-a.6.1794"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.nahs.2009.04.010"},{"key":"4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1007\/3-540-07407-4_17","volume-title":"Quantifier elimination for real closed fields by cylindrical algebraic decomposition","volume":"33","year":"1975"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7643-8539-2_2"},{"volume":"60","first-page":"xi+358","year":"1974","key":"8"},{"key":"9","first-page":"209","volume":"11","year":"2003","journal-title":"Handbook of Numerical Analysis"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1142\/9789812567727"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.2307\/1969640"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1006\/jcom.2000.0563"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.2002.0563"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1007\/s10440-012-9782-3"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1007\/s11075-012-9646-y"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1007\/s11075-009-9339-3"},{"year":"2004","key":"19"},{"year":"2001","key":"20"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/859578.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/859578.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/859578.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,22]],"date-time":"2017-06-22T00:31:17Z","timestamp":1498091477000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/859578\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":16,"alternative-id":["859578","859578"],"URL":"https:\/\/doi.org\/10.1155\/2013\/859578","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2013]]}}}