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Zbl 1228.34078
Tang, Rong-An; Liu, Ya-Li; Xue, Ju-Kui
An extended active control for chaos synchronization. (English)
[J] Phys. Lett., A 373, No. 16, 1449-1454 (2009). ISSN 0375-9601

Summary: By introducing a control strength matrix, the active control theory in chaotic synchronization is developed. With this extended method, chaos complete synchronization can be achieved more easily, i.e., a much smaller control signal is enough to reach synchronization in most cases. Numerical simulations on Rössler, Liu's four-scroll, and Chen system confirmed this and show that the synchronization result depends on the control strength significantly. Especially, in the case of Liu and Chen systems, the response systems' largest Lyapunov exponents' variation with the control strength is not monotone and there exist minima. It is novel for Chen system that the synchronization speed with a special small strength is higher than that of the usual active control which, as a special case of the extended method, has a much larger control strength. All these results indicate that the control strength is an important factor in the actual synchronization. So, with this extended active control, one can make a better and more practical synchronization scheme by adjusting the control strength matrix.

MSC 2000:: *34D06
34D08 Lyapunov exponents
34H10
34C28 Other types of "recurrent" solutions of ODE

Keywords: chaos synchronization; control strength; extended active control; Rössler system; Liu's four-scroll system; Chen system; largest Lyapunov exponent

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