{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T10:43:25Z","timestamp":1760784205570},"reference-count":29,"publisher":"World Scientific Pub Co Pte Lt","issue":"13","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2016,12,15]]},"abstract":"<jats:p> This paper develops the analytical conditions for the onset and disappearance of motion passability and sliding along an elliptic boundary in a second-order discontinuous system. A periodically forced system, described by two different linear subsystems, is considered mainly to demonstrate the methodology. The passable, sliding and grazing conditions of a flow to the elliptic boundary in the discontinuous dynamical system are provided through the analysis of the corresponding vector fields and [Formula: see text]-functions. Moreover, by constructing appropriate generic mappings, periodic orbits in such a discontinuous system are predicted analytically. Finally, three different cases are discussed to illustrate the existence of periodic orbits with passable and\/or sliding flows. The results obtained in this paper can be applied to the sliding mode control in discontinuous dynamical systems. <\/jats:p>","DOI":"10.1142\/s0218127416502242","type":"journal-article","created":{"date-parts":[[2016,12,29]],"date-time":"2016-12-29T09:22:06Z","timestamp":1483003326000},"page":"1650224","source":"Crossref","is-referenced-by-count":15,"title":["Periodic Orbits in a Second-Order Discontinuous System with an Elliptic Boundary"],"prefix":"10.1142","volume":"26","author":[{"given":"Liping","family":"Li","sequence":"first","affiliation":[{"name":"Department of Mathematics, Huzhou University, Huzhou, Zhejiang 313000, P. R.China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Albert C. 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