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Partial Contraction Analysis of Coupled Fractional Order Systems

Author

Listed:
  • Ahmad Ruzitalab
  • Mohammad Hadi Farahi
  • Gholamhossien Erjaee

Abstract

Contraction theory regards the convergence between two arbitrary system trajectories. In this article we have introduced partial contraction theory as an extension of contraction theory to analyze coupled identical fractional order systems. It can, also, be applied to study the synchronization phenomenon in networks of various structures and with arbitrary number of systems. We have used partial contraction theory to derive exact and global results on synchronization and antisynchronization of fractional order systems.

Suggested Citation

  • Ahmad Ruzitalab & Mohammad Hadi Farahi & Gholamhossien Erjaee, 2018. "Partial Contraction Analysis of Coupled Fractional Order Systems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2018(1).
    • Handle: RePEc:wly:jnljam:v:2018:y:2018:i:1:n:9414835
    DOI: 10.1155/2018/9414835
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    References listed on IDEAS

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    1. Chen, Wei-Ching, 2008. "Nonlinear dynamics and chaos in a fractional-order financial system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1305-1314.
    2. Erjaee, G.H., 2009. "On analytical justification of phase synchronization in different chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1195-1202.
    3. Leon Glass, 2001. "Synchronization and rhythmic processes in physiology," Nature, Nature, vol. 410(6825), pages 277-284, March.
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