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Generalized projective synchronization for the chaotic Lorenz system and the chaotic Chen system. (English) Zbl 1118.34050

Two systems are said to have the “projective synchronization” if their state variables x n and y n satisfy asymptotically x(t)-αy(t)0 for t and all initial conditions with some scalar α. The authors consider the following control setup in order to achieve the projective synchronization:

x ' =f(x),y ' =f(y)+u,

where the control u(x,y) is chosen in such a way that the error system admits the linear form (αy-x) ' =M(αy-x) with a stable matrix M.

MSC:
34H05ODE in connection with control problems
34C15Nonlinear oscillations, coupled oscillators (ODE)
34D35Stability of manifolds of solutions of ODE
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