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A necessary condition for double scroll attractor existence in fractional-order systems. (English) Zbl 1209.37037
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:
37D45Strange attractors, chaotic dynamics
34A08Fractional differential equations