{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T14:34:49Z","timestamp":1772289289710,"version":"3.50.1"},"reference-count":13,"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":[[2009,4]]},"abstract":"<jats:p> In this paper, we consider a planar dynamical system with a piecewise linear function containing two dropping sections and approximating some continuous nonlinear function. Studying all possible local and global bifurcations of its limit cycles, we prove that such a piecewise linear dynamical system, with five singular points, can have at most four limit cycles, three of which surround the foci one by one and the fourth limit cycle surrounds all of the singular points of this system. <\/jats:p>","DOI":"10.1142\/s021812740902369x","type":"journal-article","created":{"date-parts":[[2009,8,17]],"date-time":"2009-08-17T05:02:26Z","timestamp":1250485346000},"page":"1367-1372","source":"Crossref","is-referenced-by-count":6,"title":["A PIECEWISE LINEAR DYNAMICAL SYSTEM WITH TWO DROPPING SECTIONS"],"prefix":"10.1142","volume":"19","author":[{"given":"VALERY A.","family":"GAIKO","sequence":"first","affiliation":[{"name":"Department of Mathematics, Belarusian State University of Informatics and Radioelectronics, Leonid Beda Street 6\u20134, Minsk 220040, Belarus"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"WIM T.","family":"VAN HORSSEN","sequence":"additional","affiliation":[{"name":"Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","volume-title":"Theory of Oscillators","author":"Andronov A. A.","year":"1987"},{"key":"rf2","volume-title":"Theory of Bifurcations of Dynamic Systems on a Plane","author":"Andronov A. A.","year":"1971"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8928(74)90020-3"},{"key":"rf4","volume-title":"Methods and Ways of the Qualitative Analysis of Dynamical Systems in a Plane","author":"Bautin N. N.","year":"1990"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2005.06.029"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-7793-9"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-9168-3"},{"key":"rf8","author":"Gaiko V. A.","journal-title":"Nonlin. Anal."},{"key":"rf9","first-page":"1","volume":"1","author":"Gaiko V. A.","journal-title":"Int. J. Math. Manuscripts"},{"key":"rf10","first-page":"189","volume":"59","author":"Gaiko V. A.","journal-title":"Nonlin. Anal."},{"key":"rf11","first-page":"1","volume":"14","author":"Giannakopoulos F.","journal-title":"Nonlinearity"},{"key":"rf12","volume-title":"Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields","author":"Guckenheimer J.","year":"1990"},{"key":"rf13","volume-title":"Differential Equations and Dynamical Systems","author":"Perko L.","year":"2002"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021812740902369X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T20:02:41Z","timestamp":1565121761000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021812740902369X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,4]]},"references-count":13,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2009,4]]}},"alternative-id":["10.1142\/S021812740902369X"],"URL":"https:\/\/doi.org\/10.1142\/s021812740902369x","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,4]]}}}