Mathematical analysis and emulation of the fractional-order cubic flux-controlled memristor

Alexandria Engineering Journal

Zhang Guo¹  Gangquan Si²  Yiyuan Bie³  Babajide Oluwatosin Oresanya³  Xiang Xu³ 

[1] State Key Laboratory of Electrical Insulation and Power Equipment, Shaanxi Key Laboratory of Smart Grid, School of Electrical Engineering, Xi’an Jiaotong University, Xi’an, Shaaanxi Province 710049, China;Corresponding author at: The Electrical Engineering School of Xi’an Jiaotong University, 28 West Xianning Road, Xi’an, Shaanxi Province 710049, China.;State Key Laboratory of Electrical Insulation and Power Equipment, Shaanxi Key Laboratory of Smart Grid, School of Electrical Engineering, Xi’an Jiaotong University, Xi’an, Shaaanxi Province 710049, China;

关键词: Memristor emulator;    Fractional-order memristor;    Cubic model;    Intersection points;   

DOI  :  

来源: DOAJ

【 摘 要 】

Cubic model of flux-controlled memristor model is presented in this work and the model is analyzed at various fractional orders. Analytic computations with a sinusoidal source shows that the v-i loop can have up to two more additional intersection points aside from the origin and are located in the 1st and 3rd quadrants respectively. The locations of the intersection points and the area of the v-i loops are both dependent on the excitation signal frequency and fractional orders. Floating and Grounded emulator circuits for the cubic models are designed incorporating a fractional order integrator designed from the 2nd-order rational approximation of s-α. PSPICE simulations verify the correctness of the numerical analysis and calculations. An application example shows that the fractional-order cubic model can generate chaos in Chua’s circuit and produced an increase in the system dynamics.

【 授权许可】

Unknown