{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T07:21:00Z","timestamp":1770448860153,"version":"3.49.0"},"reference-count":23,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2016,2]]},"abstract":"<jats:p> In this paper, we extend the well-known Melnikov method for smooth systems to a class of periodic perturbed planar hybrid piecewise-smooth systems. In this class, the switching manifold is a straight line which divides the plane into two zones, and the dynamics in each zone is governed by a smooth system. When a trajectory reaches the separation line, then a reset map is applied instantaneously before entering the trajectory in the other zone. We assume that the unperturbed system is a piecewise Hamiltonian system which possesses a piecewise-smooth homoclinic solution transversally crossing the switching manifold. Then, we study the persistence of the homoclinic orbit under a nonautonomous periodic perturbation and the reset map. To achieve this objective, we obtain the Melnikov function to measure the distance of the perturbed stable and unstable manifolds and present the theorem for homoclinic bifurcations for the class of planar hybrid piecewise-smooth systems. Furthermore, we employ the obtained Melnikov function to detect the chaotic boundaries for a concrete planar hybrid piecewise-smooth system. <\/jats:p>","DOI":"10.1142\/s0218127416500309","type":"journal-article","created":{"date-parts":[[2016,3,10]],"date-time":"2016-03-10T03:26:20Z","timestamp":1457580380000},"page":"1650030","source":"Crossref","is-referenced-by-count":21,"title":["Melnikov Method for a Class of Planar Hybrid Piecewise-Smooth Systems"],"prefix":"10.1142","volume":"26","author":[{"given":"Shuangbao","family":"Li","sequence":"first","affiliation":[{"name":"College of Science, Civil Aviation University of China, Tianjin 300300, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wensai","family":"Ma","sequence":"additional","affiliation":[{"name":"College of Science, Civil Aviation University of China, Tianjin 300300, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, Beijing University of Technology, Beijing 100022, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuxin","family":"Hao","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, Beijing Information Science and Technology University, Beijing 100192, P. R. 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