Dynamical Analysis of the Generalized Lorenz Systems

In this paper, global attractive sets of the generalized Lorenz system are studied according to Lyapunov stability theory and optimization theory. The method of constructing Lyapunov functions applied to the former chaotic dynamical systems is not applicable to the generalized Lorenz system. We overcome this difficulty by adding a cross term to the Lyapunov functions of the generalized Lorenz system.

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