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Zbl 1209.37037
Tavazoei, Mohammad Saleh; Haeri, Mohammad
A necessary condition for double scroll attractor existence in fractional-order systems. (English)
[J] Phys. Lett., A 367, No. 1-2, 102-113 (2007). ISSN 0375-9601

Summary: 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.

MSC 2000:: *37D45 Strange attractors, chaotic dynamics
34A08

Keywords: fractional-order system; chaotic system; Chen system; Lü system

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Zentralblatt MATH Berlin [Germany]