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Synchronization and Anti-synchronization of Fractional Order Chaotic Systems by Means of a Fractional Integral Observer

  • Rafael Martínez-GuerraEmail author
  • Claudia Alejandra Pérez-Pinacho
Chapter
Part of the Understanding Complex Systems book series (UCS)

Abstract

The problem of anti-synchronization is another phenomenon of interest that occurs in chaotic oscillators. This problem has appeared in modern repetitions of Huygens’ experiments (Bennett et al., Proc: Math Phys Eng Sci 458:563–579, 2002, [2]), lasers (Uchida et al., Phys Rev A 64:023801-1–023801-6, 2001, [2]), (Wedekind and Parlitz, Int J Bifurc Chaos 11(4):1141–1147, 2001, [3]), saltwater oscillators (Nakata et al., Phys D 115:313–320, 1998, [4]), and some biological systems where a nonchaotic signal is generated (Kim et al., Phys Lett A 320:39–46, 2003, [5]). Anti-synchronization has been treated as a direct modification of synchronization, simply with a sign change in the condition required for the error, and has been attacked with methods such as the active control (Emadzadeh and Haeri, Int J Electr Comput Energ Electron Commun Eng 1(6):898–901, 2007, [6]) (Guo-Hui, Chaos, Solitons Fractals 26:87–93, 2005, [7]) and the sliding mode control (Chen et al., Nonlinear Dyn 69:35–55, 2012, [8]). It can also be induced by noise (Kawamura, Phys D 270(1):20–29, 2014, [9]).

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Rafael Martínez-Guerra
    • 1
    Email author
  • Claudia Alejandra Pérez-Pinacho
    • 1
  1. 1.Automatic ControlCINVESTAV-IPNMexico CityMexico

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