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

作者：Tavazoei Mohammad Saleh; Haeri Mohammad^*

来源：Physics Letters, Section A: General, Atomic and Solid State Physics , 2007, 367(1-2): 102-113.

DOI：10.1016/j.physleta.2007.05.081

• fractional-order system
• chaotic system
• Chen system
• Lu system

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 Lu 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.

• 出版日期2007-7-16