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Dynamics including the multistability of the system with the variation of system parameters and the derivative order are investigated by Lyapunov exponents (LEs), bifurcation diagram, phase portrait, entropy measure, and basins of attraction, numerically. It shows that the minimum order for chaos of the fractional-order centrifugal flywheel governor system is q\u2009=\u20090.97, and the system has rich dynamics and produces multiple coexisting attractors. Moreover, the system is controlled by introducing the adaptive controller which is proved by the Lyapunov stability theory. Numerical analysis results verify the effectiveness of the proposed method.<\/jats:p>","DOI":"10.1155\/2020\/8844657","type":"journal-article","created":{"date-parts":[[2020,12,14]],"date-time":"2020-12-14T18:35:16Z","timestamp":1607970916000},"page":"1-11","source":"Crossref","is-referenced-by-count":5,"title":["Multistability in a Fractional-Order Centrifugal Flywheel Governor System and Its Adaptive Control"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6498-5767","authenticated-orcid":true,"given":"Bo","family":"Yan","sequence":"first","affiliation":[{"name":"College of Electrical and Information Engineering, Shaoyang University, Shaoyang 422000, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5190-4841","authenticated-orcid":true,"given":"Shaobo","family":"He","sequence":"additional","affiliation":[{"name":"School of Physics and Electronics, Central South University, Changsha 410083, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1529-8287","authenticated-orcid":true,"given":"Shaojie","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Electrical and Information Engineering, Shaoyang University, Shaoyang 422000, China"}]}],"member":"311","reference":[{"volume-title":"Mathematics for Dynamic Modeling","year":"1987","author":"E. 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