Hopf bifurcation and chaos in a fractional order delayed memristor-based chaotic circuit system

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• 作者：Wei Hu ; Dawei Ding ; ^{dwding@ahu.edu.cn} ; Yaqin Zhang ; Nian Wang ; Dong Liang
• 关键词：Hopf bifurcation ; Chaos ; Stability ; Time delay ; Fractional order ; Memristor
• 刊名：Optik - International Journal for Light and Electron Optics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：130
• 期：Complete
• 页码：189-200
• 全文大小：2347 K
• 卷排序：130

文摘

This paper present Hopf bifurcation and chaos in a fractional order delayed memristor-based chaotic circuit system. Firstly, regarding the time delay ττ as a bifurcation parameter, we investigate the stability and bifurcation behaviors of this fractional order delayed memristor-based chaotic circuit system. Some explicit conditions for describing the stability interval and emergence of Hopf bifurcation are derived. Secondly, corresponding to different system parameters, the complex dynamics behaviors of this system are discussed by using the bifurcation diagrams, the Max Lyapunov exponents (MLEs) diagram, the time domain waveforms, the phase portraits and the power spectrums. Thirdly, we study the influence of the two parameters (time delay ττ and fractional order qq) on the chaotic behavior, and it is found when time delay ττ and fractional order qq increases, the transitions from period one to period two and period four to chaos are observed in this memristor–based system. Meanwhile, corresponding critical values of time delay ττ and fractional order qq, the lowest orders qq and the minimum time delay ττ for generating chaos in the fractional order delayed memristor–based system are determined, respectively. Also, when the system occurs period one, the corresponding frequency is verified theoretically and experimentally. Finally, numerical simulations are provided to demonstrate the validity of theoretical analysis using the improved Adams–Bashforth–Moulton algorithm.