A new approach to generalized chaos synchronization based on the stability of the error system. (English) Zbl 1172.93015

Summary: With a chaotic system being divided into linear and nonlinear parts, a new approach is presented to realize generalized chaos synchronization by using feedback control and parameter commutation. Based on a linear transformation, the problem of Generalized Synchronization (GS) is transformed into the stability problem of the synchronous error system, and an existence condition for GS is derived. Furthermore, the performance of GS can be improved according to the configuration of the GS velocity. Further generalization and appropriation can be acquired without a stability requirement for the chaotic system’s linear part. The Lorenz system and a hyperchaotic system are taken for illustration and verification and the results of the simulation indicate that the method is effective.


93B55 Pole and zero placement problems
93C10 Nonlinear systems in control theory
37N35 Dynamical systems in control
58E25 Applications of variational problems to control theory
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