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Zbl 0823.93026
Čelikovský, Sergej; Vaněček, Antonín
Bilinear systems and chaos. (English)
[J] Kybernetika 30, No.4, 403-424 (1994). ISSN 0023-5954

Motivated by the chaotic behavior of Lorenz equations, the authors presents a conjecture on chaos in a bilinear system in $\bbfR\sp 3$ of the form $\dot x= Ax+ Bxu$, $x\in \bbfR\sp 3$, $u\in \bbfR$. The main results of this article are two theorems on the existence of a pair of symmetric homoclinic orbits and on the chaotic behavior of a generalized Lorenz equation (GLE). The computer simulation shows that the GLE has a chaotic behavior similar to the Lorenz equation although there is some difference between the theoretical analysis and the numerical simulation.
[Ge Weigao (Beijing)]

MSC 2000:: *93C15 Control systems governed by ODE
37D45 Strange attractors, chaotic dynamics

Keywords: skew-symmetry; eigenvalue; bilinear system; homoclinic orbits; chaotic behavior; numerical simulation

Cited in: Zbl 1043.37023

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