{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T21:58:48Z","timestamp":1765231128604,"version":"3.37.3"},"reference-count":35,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","funder":[{"name":"National Natural Science Foundation of China (CN)","award":["11671149"],"award-info":[{"award-number":["11671149"]}]},{"DOI":"10.13039\/501100003453","name":"Natural Science Foundation of Guangdong Province","doi-asserted-by":"publisher","award":["2017A030312006"],"award-info":[{"award-number":["2017A030312006"]}],"id":[{"id":"10.13039\/501100003453","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61527811"],"award-info":[{"award-number":["61527811"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2019,5]]},"abstract":"<jats:p> In the chaotic polynomial Lorenz-type systems (including Lorenz, Chen, L\u00fc and Yang systems) and R\u00f6ssler system, their equilibria are unstable and the number of the hyperbolic equilibria are no more than three. This paper shows how to construct a simple analytic (nonpolynomial) chaotic system that can have any preassigned number of equilibria. A special 3D chaotic system with no equilibrium is first presented and discussed. Using a methodology of adding a constant controller to the third equation of such a chaotic system, it is shown that a chaotic system with any preassigned number of equilibria can be generated. Two complete mathematical characterizations for the number and stability of their equilibria are further rigorously derived and studied. This system is very interesting in the sense that some complex dynamics are found, revealing many amazing properties: (i) a hidden chaotic attractor exists with no equilibria or only one stable equilibrium; (ii) the chaotic attractor coexists with unstable equilibria, including two\/five unstable equilibria; (iii) the chaotic attractor coexists with stable equilibria and unstable equilibria, including one stable and two unstable equilibria\/94 stable and 93 unstable equilibria; (iv) the chaotic attractor coexists with infinitely many nonhyperbolic isolated equilibria. These results reveal an intrinsic relationship of the global dynamical behaviors with the number and stability of the equilibria of some unusual chaotic systems. <\/jats:p>","DOI":"10.1142\/s0218127419500603","type":"journal-article","created":{"date-parts":[[2019,6,3]],"date-time":"2019-06-03T23:42:25Z","timestamp":1559605345000},"page":"1950060","source":"Crossref","is-referenced-by-count":22,"title":["Constructing a New 3D Chaotic System with Any Number of Equilibria"],"prefix":"10.1142","volume":"29","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3623-4947","authenticated-orcid":false,"given":"Qigui","family":"Yang","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, South China University of Technology, Guangzhou, Guangdong 510641, P. R. China"}]},{"given":"Xinmei","family":"Qiao","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, South China University of Technology, Guangzhou, Guangdong 510641, P. R. 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