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Passive and impulsive synchronization of a new four-dimensional chaotic system. (English) Zbl 1216.34048
Two control methods are investigated for the synchronization of two identical four-dimensional chaotic Qi systems interacting according to the drive-response coupling scheme. It is shown that the driving signal can be constructed in such a way that the corresponding system for the synchronization error becomes passive with respect to the input. This proves the asymptotic stability of the trivial equilibrium of the synchronization error system and, thus, the onset of synchronization between the drive and response chaotic Qi systems. The second considered method is based on the impulsive control technique of synchronization. Sufficient conditions for the global asymptotic stability of the chaotic synchronization are derived. The analytical results are illustrated by numerical simulations.
MSC:
34D06Synchronization
34H05ODE in connection with control problems
34C28Complex behavior, chaotic systems (ODE)
34D20Stability of ODE
34H10Chaos control (ODE)
34A37Differential equations with impulses
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