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Manipulating the scaling factor of projective synchronization in three-dimensional chaotic systems. (English) Zbl 0996.37075

Summary: The scaling factor characterizes the synchronized dynamics of projective synchronization in partially linear chaotic systems but it is difficult to be estimated. To manipulate projective synchronization of chaotic systems in a favored way, a control algorithm is introduced to direct the scaling factor onto a desired value. The control approach is derived from the Lyapunov stability theory. It allows us to arbitrarily amplify or reduce the scale of the response of the slave system via a feedback control on the master system. In numerical experiments, we illustrate the application to the Lorenz system.

MSC:

37M05 Simulation of dynamical systems
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C60 Qualitative investigation and simulation of ordinary differential equation models
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