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Volume 6, Number 4, 2016, Pages 1049-1063                                                                DOI:10.11948/2016068
Control And Synchronization Of Julia Sets Generated By A Class Of Complex Time-delay Rational Map
Da Wang,Shutang Liu,Kexin Liu,Yang Zhao
Keywords:Time-delay complex system, julia set, control, synchronization.
      In this paper, a class of complex time-delay rational map is studied by analyzing the fractal and dynamical properties of its corresponding Julia sets (CTRM-Julia sets for short). By utilizing these given properties, a hybrid control method which contains both state feedback and parameters perturbation is applied to achieve the boundary control of CTRM-Julia set. Moreover, the synchronization of two different CTRM-Julia sets is also investigated by using coupling method. The synchronization index method is applied to demonstrate the relationship between the degree of synchronization and the coupling strength. Numerical examples are given to verify the effectiveness of control and synchronization methods.
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