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Adaptive Synchronization between Fractional-Order Chaotic Real and Complex Systems with Unknown Parameters

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  • Xiaomin Tian

Abstract

The complex modified projective synchronization (CMPS) between fractional-order chaotic real and complex systems is investigated for the first time. The parameters of both master and slave systems are assumed to be unknown in advance; moreover, the slave system is perturbed by unknown but bounded external disturbances. The master and slave systems that achieved CMPS can be synchronized up to a complex constant matrix. On the basis of frequency distributed model of fractional integrator and Lyapunov stability theory, a robust adaptive control law is designed to realize the CMPS for two different types of fractional-order chaotic systems. Meanwhile, to deal with these unknown parameters, some fractional-order type parametric update laws are provided. An example is given to demonstrate the effectiveness and feasibility of the proposed synchronization scheme.

Suggested Citation

  • Xiaomin Tian, 2014. "Adaptive Synchronization between Fractional-Order Chaotic Real and Complex Systems with Unknown Parameters," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-11, November.
    • Handle: RePEc:hin:jnddns:484039
    DOI: 10.1155/2014/484039
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