Generalized synchronization in chaotic systems
Let there be a drive system \(dx/dt=f(x), \;x\in \mathbb{R}^n\), and a function \(H: \mathbb{R}^n \rightarrow \mathbb{R}^m\). 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.
scientific article; zbMATH DE number 1370456