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Bilinear systems and chaos. (English) Zbl 0823.93026
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.

93C15Control systems governed by ODE
37D45Strange attractors, chaotic dynamics
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