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Stabilizing periodic orbits of fractional order chaotic systems via linear feedback theory

Rahim,i M. A ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1016/j.apm.2011.07.019
  3. Abstract:
  4. In this paper stabilizing unstable periodic orbits (UPO) in a chaotic fractional order system is studied. Firstly, a technique for finding unstable periodic orbits in chaotic fractional order systems is stated. Then by applying this technique to the fractional van der Pol and fractional Duffing systems as two demonstrative examples, their unstable periodic orbits are found. After that, a method is presented for stabilization of the discovered UPOs based on the theories of stability of linear integer order and fractional order systems. Finally, based on the proposed idea a linear feedback controller is applied to the systems and simulations are done for demonstration of controller performance
  5. Keywords:
  6. Chaos ; Fractional order system ; Unstable periodic orbit ; Controller performance ; Duffing system ; Fractional-order chaotic systems ; Fractional-order systems ; Integer order ; Linear feedback ; Linear feedback controllers ; Linear stability theory ; Periodic orbits ; Van der Pol ; Algebra ; Chaos theory ; Control ; Orbits ; Stabilization ; Chaotic systems
  7. Source: Applied Mathematical Modelling ; Vol. 36, Issue 3 , 2012 , pp. 863-877 ; ISSN: 0307904X
  8. URL: http://www.sciencedirect.com/science/article/pii/S0307904X11003994