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The investigation shows that the nonlinear oscillator exhibits complex equilibrium bifurcations of single-, double-, triple- and quadruple-well properties, and the singular closed orbits of homoclinic, heteroclinic and homo-heteroclinic types as well for both smooth and discontinuous cases. The chaotic behaviors are also presented numerically for the perturbed system under the perturbation of both viscous-damping and external excitation. This oscillator can be extended to a high-order-quasi-zero-stiffness isolator and a nonlinear supporting system for ground vibration test for large-scale structures to achieve the high-static-low-dynamic-stiffness. <\/jats:p>","DOI":"10.1142\/s0218127415300384","type":"journal-article","created":{"date-parts":[[2016,1,5]],"date-time":"2016-01-05T03:43:16Z","timestamp":1451965396000},"page":"1530038","source":"Crossref","is-referenced-by-count":35,"title":["Nonlinear Dynamics of a Smooth and Discontinuous Oscillator with Multiple Stability"],"prefix":"10.1142","volume":"25","author":[{"given":"Yanwei","family":"Han","sequence":"first","affiliation":[{"name":"Centre for Nonlinear Dynamics Research, Harbin Institute of Technology, School of Astronautics, Harbin 150001, P. R. 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