{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T23:39:38Z","timestamp":1775173178633,"version":"3.50.1"},"reference-count":52,"publisher":"World Scientific Pub Co Pte Ltd","issue":"07","funder":[{"DOI":"10.13039\/501100005230","name":"the Natural Science Foundation of Chongqing","doi-asserted-by":"crossref","award":["CSTB2022NSCQ-MSX1548"],"award-info":[{"award-number":["CSTB2022NSCQ-MSX1548"]}],"id":[{"id":"10.13039\/501100005230","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12371137"],"award-info":[{"award-number":["12371137"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Scientific and Technological Research Program of Chongqing Municipal Education Commission","award":["KJQN202100813"],"award-info":[{"award-number":["KJQN202100813"]}]},{"name":"the Scientific and Technological Research Program of Chongqing Municipal Education Commission","award":["KJQN201800818"],"award-info":[{"award-number":["KJQN201800818"]}]},{"name":"the Scientific and Technological Research Program of Chongqing Municipal Education Commission","award":["KJCX2020037"],"award-info":[{"award-number":["KJCX2020037"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2024,6,15]]},"abstract":"<jats:p> In this paper, the qualitative properties of a physically extended six-dimensional Lorenz system, with additional physical terms describing rotation and density, which was proposed in [Moon et al., 2019] have been investigated. The dissipation, invariance, Lyapunov exponents, Kaplan\u2013Yorke dimension, ultimate boundedness and global attractivity of this six-dimensional Lorenz system have been discussed in detail according to the chaotic systems theory. We find that this system exhibits chaos phenomena for a new set of parameters. It is well known that the general method for studying the bounds of a chaotic system is to construct a suitable Lyapunov-like function (or the generalized positive definite and radically unbounded Lyapunov function). However, the higher the dimension of a chaotic system, the more difficult it is to construct the Lyapunov-like function. The innovation of this paper is that we first construct the suitable Lyapunov-like function for this six-dimensional Lorenz system, and then we prove that this system is not only globally bounded for varying parameters, but it also gives a collection of global absorbing sets for this system with respect to all parameters of this system according to Lyapunov\u2019s direct method and the optimization method. Furthermore, we obtain the rate of the trajectories going from the exterior to the global absorbing set. Some numerical simulations are presented to validate our research results. Finally, we give a direct application of the results obtained in this paper. According to the results of this paper, we can conclude that the equilibrium point [Formula: see text] of this system is globally exponentially stable. <\/jats:p>","DOI":"10.1142\/s0218127424500834","type":"journal-article","created":{"date-parts":[[2024,5,25]],"date-time":"2024-05-25T04:14:06Z","timestamp":1716610446000},"source":"Crossref","is-referenced-by-count":1,"title":["Qualitative Properties of a Physically Extended Six-Dimensional Lorenz System"],"prefix":"10.1142","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8999-7569","authenticated-orcid":false,"given":"Fuchen","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Chongqing Key Laboratory of Statistical Intelligent Computing and Monitoring, Chongqing Technology and Business University, Chongqing 400067, P. R. 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