{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T02:10:18Z","timestamp":1773713418813,"version":"3.50.1"},"reference-count":23,"publisher":"World Scientific Pub Co Pte Ltd","issue":"10","funder":[{"DOI":"10.13039\/501100001809","name":"the Natural Science Foundation of China","doi-asserted-by":"crossref","award":["(Nos. 11872253"],"award-info":[{"award-number":["(Nos. 11872253"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"the Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11602151"],"award-info":[{"award-number":["11602151"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"the Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11772007"],"award-info":[{"award-number":["11772007"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"the Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11790282"],"award-info":[{"award-number":["11790282"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Natural Science Foundation for Outstanding Young Researcher in Hebei Province of China","award":["A2017210177"],"award-info":[{"award-number":["A2017210177"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2020,8]]},"abstract":"<jats:p> In smooth systems, the form of the heteroclinic Melnikov chaotic threshold is similar to that of the homoclinic Melnikov chaotic threshold. However, this conclusion may not be valid in nonsmooth systems with jump discontinuities. In this paper, based on a newly constructed nonsmooth pendulum, a kind of impulsive differential system is introduced, whose unperturbed part possesses a nonsmooth heteroclinic solution with multiple jump discontinuities. Using the recursive method and the perturbation principle, the effects of the nonsmooth factors on the behaviors of the nonsmooth dynamical system are converted to the integral items which can be easily calculated. Furthermore, the extended Melnikov function is employed to obtain the nonsmooth heteroclinic Melnikov chaotic threshold, which implies that the existence of the nonsmooth heteroclinic orbits may be due to the breaking of the nonsmooth heteroclinic loops under the perturbation of damping, external forcing and nonsmooth factors. It is worth pointing out that the form of the nonsmooth heteroclinic Melnikov function is different from the one of the nonsmooth homoclinic Melnikov function, which is quite different from the classical Melnikov theory. <\/jats:p>","DOI":"10.1142\/s0218127420501412","type":"journal-article","created":{"date-parts":[[2020,9,1]],"date-time":"2020-09-01T09:20:57Z","timestamp":1598952057000},"page":"2050141","source":"Crossref","is-referenced-by-count":16,"title":["Heteroclinic Chaotic Threshold in a Nonsmooth System with Jump Discontinuities"],"prefix":"10.1142","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4538-9094","authenticated-orcid":false,"given":"R. L.","family":"Tian","sequence":"first","affiliation":[{"name":"State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043, P. R. China"},{"name":"Key Laboratory of Smart Materials and Structures Mechanics, Hebei Province, 050043, P. R. China"},{"name":"Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang 050043, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"T.","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043, P. R. China"},{"name":"Key Laboratory of Smart Materials and Structures Mechanics, Hebei Province, 050043, P. R. China"},{"name":"Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang 050043, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Y. 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