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Zbl 0946.34040
Yang, S.S.; Duan, C.K.
Generalized synchronization in chaotic systems. (English)
[J] Chaos Solitons Fractals 9, No.10, 1703-1707 (1998). ISSN 0960-0779

Let there be a drive system $dx/dt=f(x), \ x\in \bbfR^n$, and a function $H: \bbfR^n \rightarrow \bbfR^m$. The goal is to construct a response system $dy/dt = g(u(x),y)$ with the drive function $u$ such that $||y(t, y_0) - H(x(t,x_0))||\rightarrow 0$ as $t \rightarrow \infty$ (generalized synchronization). The author proves that the asymptotic stability of the linearized system $d\eta /dt = g_y (H(x (t,x_0), u(x(t,x_0))))\eta$ implies generalized synchronization.
[Klaus R.Schneider (Berlin)]

MSC 2000:: *34C28 Other types of "recurrent" solutions of ODE
34D05 Asymptotic stability of ODE

Keywords: generalized synchronization; chaotic systems; asymptotic behavior

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