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Zbl 1043.37023
Čelikovský, Sergej; Chen, Guanrong
On a generalized Lorenz canonical form of chaotic systems. (English)
[J] Int. J. Bifurcation Chaos Appl. Sci. Eng. 12, No. 8, 1789-1812 (2002). ISSN 0218-1274

Summary: This paper shows that a large class of systems, as the so-called generalized Lorenz system, are state-equivalent to a special canonical form that covers a broader class of chaotic systems. This canonical form, called generalized Lorenz canonical form hereafter, generalizes the one introduced and analyzed in [{\it S. Čelikovský} and {\it S. Vaněček}, Kybernetika 30, 403--424 (1994; Zbl 0823.93026) and Control systems. From linear analysis to synthesis of chaos, London: Prentice Hall (1996; Zbl 0874.93006)], and also covers the so-called Chen system, recently introduced in [{\it G. Chen} and {\it T. Ueta}, ibid. 9, 1465--1466 (1999; Zbl 0962.37013) and ibid. 10, 1917--1931 (2000)]. \par Thus, this new generalized Lorenz canonical form contains as special cases the original Lorenz system, the generalized Lorenz system, and the Chen system, so that a comparison of the structures between two essential types of chaotic systems becomes possible. The most important property of the new canonical form is the parametrization that has precisely a single scalar parameter useful for chaos tuning, which has promising potential in future engineering chaos design. Some other closely related topics are studied and discussed, too.

MSC 2000:: *37D45 Strange attractors, chaotic dynamics
34C28 Other types of "recurrent" solutions of ODE
34H05 ODE in connection with control problems
93B10 Canonical structure of systems
37N05 Dynamical systems in classical and celestial mechanics
93C10 Nonlinear control systems

Keywords: Chaos; Lorenz system; Chen system; canonical form; chaos design; numerical simulation; controlling the Duffin oscillator; bifurcation; chaos synthesis

Citations: Zbl 0823.93026; Zbl 0874.93006; Zbl 0962.37013

Cited in: Zbl 1142.70012

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