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The homoclinic orbit continuously crosses the first switching manifold and transversally jumps across the second switching manifold by the impulsive effect. The trajectory of the corresponding perturbed system crosses the first switching manifold by applying the reset map describing the impact rule instantaneously. Then, the random Melnikov process of such systems is derived and the criteria for the onset of chaos with or without noise excitation are established. In addition, the complicated dynamics of concrete piecewise-smooth systems with or without noise excitation under the reset maps, impulsive effect, and non-autonomous periodic and damping perturbations are investigated by this extended method and numerical simulations.<\/jats:p>","DOI":"10.1063\/5.0096086","type":"journal-article","created":{"date-parts":[[2022,7,12]],"date-time":"2022-07-12T17:10:08Z","timestamp":1657645808000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":17,"title":["Melnikov-type method for a class of hybrid piecewise-smooth systems with impulsive effect and noise excitation: Homoclinic orbits"],"prefix":"10.1063","volume":"32","author":[{"given":"Yuxi","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematics and Physics, China University of Geosciences 1 , Wuhan 430074, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6981-748X","authenticated-orcid":false,"given":"Zhouchao","family":"Wei","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, China University of Geosciences 1 , Wuhan 430074, China"},{"name":"Zhejiang Institute, China University of Geosciences 2 , Hangzhou, Zhejiang 311305, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0210-5642","authenticated-orcid":false,"given":"Wei","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, Beijing University of Technology 3 , Beijing 100124, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ming","family":"Yi","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, China University of Geosciences 1 , Wuhan 430074, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2022,7,12]]},"reference":[{"key":"2023080921211787300_c1","volume-title":"Nonsmooth Mechanics","year":"1999"},{"key":"2023080921211787300_c2","volume-title":"Engineering Applications of Non-Smooth Dynamics","year":"2012"},{"key":"2023080921211787300_c3","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1126\/science.267326","article-title":"Oscillation and chaos in physiological control systems","volume":"197","year":"1977","journal-title":"Science"},{"key":"2023080921211787300_c4","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1137\/S1052623403422285","article-title":"Excessive gap technique in nonsmooth convex minimization","volume":"16","year":"2005","journal-title":"SIAM J. 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