Yang, Qigui; Chen, Guanrong A chaotic system with one saddle and two stable node-foci. (English) Zbl 1147.34306 Int. J. Bifurcation Chaos Appl. Sci. Eng. 18, No. 5, 1393-1414 (2008). Summary: This paper reports the finding of a chaotic system with one saddle and two stable node-foci in a simple three-dimensional (3D) autonomous system. The system connects the original Lorenz system and the original Chen system and represents a transition from one to the other. The algebraical form of the chaotic attractor is very similar to the Lorenz-type systems but they are different and, in fact, nonequivalent in topological structures. Of particular interest is the fact that the chaotic system has a chaotic attractor, one saddle and two stable node-foci. To further understand the complex dynamics of the system, some basic properties such as Lyapunov exponents, bifurcations, routes to chaos, periodic windows, possible chaotic and periodic-window parameter regions, and the compound structure of the system are analyzed and demonstrated with careful numerical simulations. Cited in 85 Documents MSC: 34A34 Nonlinear ordinary differential equations and systems 34C28 Complex behavior and chaotic systems of ordinary differential equations 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 34C23 Bifurcation theory for ordinary differential equations 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior PDF BibTeX XML Cite \textit{Q. Yang} and \textit{G. Chen}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 18, No. 5, 1393--1414 (2008; Zbl 1147.34306) Full Text: DOI References: [1] Barnett S., Polynomials and Linear Control Systems (1983) · Zbl 0528.93003 [2] Čelikovský S., Kybernetika 30 pp 403– [3] DOI: 10.1142/S0218127402005467 · Zbl 1043.37023 [4] DOI: 10.1016/j.chaos.2005.02.040 · Zbl 1100.37016 [5] DOI: 10.1142/S0218127499001024 · Zbl 0962.37013 [6] DOI: 10.1016/j.chaos.2003.10.009 · Zbl 1045.37014 [7] DOI: 10.1142/S0218127402004620 · Zbl 1063.34510 [8] DOI: 10.1142/S021812740200631X · Zbl 1043.37026 [9] DOI: 10.1090/S0273-0979-1995-00558-6 · Zbl 0820.58042 [10] Oselede V. I., Trudy Moskov. Mat. Obshch. 19 pp 179– [11] DOI: 10.1007/978-1-4612-5767-7 [12] Sprott J. C., Chaos and Time-Series Analysis (2003) · Zbl 1012.37001 [13] DOI: 10.1038/35023206 [14] DOI: 10.1016/S0764-4442(99)80439-X · Zbl 0935.34050 [15] Ueta T., Int. J. Bifurcation and Chaos 10 pp 1917– [16] Vanečěk A., Control Systems: From Linear Analysis to Synthesis of Chaos (1996) [17] R. Williams, Turbulence Seminar Berkeley 1996/97, eds. P. Bermard and T. Ratiu (Springer-Verlag, Berlin, 1997) pp. 94–112. [18] DOI: 10.1142/S0218127406016501 · Zbl 1185.37088 [19] DOI: 10.1142/S0218127407019792 · Zbl 1149.37308 [20] DOI: 10.1142/S0218127403008089 · Zbl 1046.37018 [21] DOI: 10.1142/S0218127404011296 · Zbl 1129.37326 [22] DOI: 10.1016/j.chaos.2003.10.030 · Zbl 1048.37032 [23] DOI: 10.1016/S0960-0779(03)00243-1 · Zbl 1053.37016 [24] DOI: 10.1007/s11071-005-4195-8 · Zbl 1142.70012 [25] DOI: 10.1142/S0218127406016203 · Zbl 1185.37092 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.