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 $1\text{st}$ and $3\text{rd}$ 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 $2\text{nd}$-order rational approximation of $s^{-\alpha }$. 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.

提出了磁通控制忆阻器模型的三次模型，并对模型进行了不同的分数阶分析。用正弦波源进行的解析计算表明，$v--\mathrm{一世}$ 循环除了原点外最多可以有两个其他的相交点，它们位于 $\mathrm{1个}\text{英石}$ 和 $3\text{rd}$象限。相交点的位置和区域$v--\mathrm{一世}$环路都取决于激励信号的频率和分数阶。三次模型的浮动和接地仿真器电路设计为结合了一个由分数阶积分器设计的分数阶积分器。$\mathrm{2个}\text{nd}$的阶有理逼近 $s^{--\alpha }$。PSPICE仿真验证了数值分析和计算的正确性。一个应用实例表明，分数阶三次模型可以在蔡氏电路中产生混乱，并增加了系统动力学。