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A necessary condition for double scroll attractor existence in fractional-order systems

Tavazoei, M. S ; Sharif University of Technology | 2007

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  1. Type of Document: Article
  2. DOI: 10.1016/j.physleta.2007.05.081
  3. Publisher: Elsevier , 2007
  4. Abstract:
  5. In this Letter, based on the stability theorem in fractional differential equations, a necessary condition is given to check existence of double scroll attractor in a fractional-order system. Numerical simulations are presented to evaluate accuracy of this condition in fractional-order Chen and Lü systems. Also, we show that using frequency domain approximation in the numerical simulations of fractional systems may result in wrong consequences. For example, this approximation can numerically demonstrate chaos in the non-chaotic fractional-order systems. Unfortunately, this mistake has occurred in the recent literature that found the lowest-order chaotic systems among fractional-order systems. © 2007 Elsevier B.V. All rights reserved
  6. Keywords:
  7. Algebra ; Differential equations ; Frequency domain analysis ; Numerical models ; Chaotic fractional-order systems ; Chen system ; Double-scroll attractors ; Fractional differential equations ; Fractional systems ; Fractional-order systems ; Frequency domains ; Stability theorems ; Chaotic systems
  8. Source: Physics Letters, Section A: General, Atomic and Solid State Physics ; Volume 367, Issue 1-2 , 2007 , Pages 102-113 ; 03759601 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0375960107008237