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Synchronization of Chaotic Liouvillian Systems: An Application to Chua’s Oscillator

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Synchronization of Integral and Fractional Order Chaotic Systems

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

In this chapter, we deal with the synchronization of chaotic oscillators with Liouvillian properties (chaotic Liouvillian system) based on a nonlinear observer design. The strategy consists in proposing a polynomial observer (slave system) that tends to follow exponentially the chaotic oscillator (master system). The proposed technique is applied in the synchronization of Chua’s circuit. Simulation and experimental results are used to visualize and illustrate the effectiveness of the proposed scheme in synchronization.

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Notes

  1. 1.

    Mathematically, chaotic systems are characterized by local instability and global boundedness of the trajectories, i.e., \(\|x(t)\|\) is bounded for all t ≥ 0.

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Authors and Affiliations

  1. Departamento de Control Automatico, CINVESTAV-IPN, Mexico, D.F., Mexico

    Rafael Martínez-Guerra, Claudia A. Pérez-Pinacho & Gian Carlo Gómez-Cortés

Authors
  1. Rafael Martínez-Guerra
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  2. Claudia A. Pérez-Pinacho
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  3. Gian Carlo Gómez-Cortés
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Martínez-Guerra, R., Pérez-Pinacho, C.A., Gómez-Cortés, G.C. (2015). Synchronization of Chaotic Liouvillian Systems: An Application to Chua’s Oscillator. In: Synchronization of Integral and Fractional Order Chaotic Systems. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-15284-4_8

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