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物理忆阻器具有不对称的紧磁滞回线, 为了更加简便地模拟物理忆阻器的不对称紧磁滞曲线, 本文提出了一种含有偏置电压源的分数阶二极管桥忆阻器模型, 其具有可连续调控磁滞回线的能力. 首先, 结合分数阶微积分理论, 建立了含有偏置电压源的二极管桥忆阻器的分数阶模型, 并对其电气特性进行分析. 其次, 将其与Jerk混沌电路相融合, 建立了含有偏置电压源的非齐次分数阶忆阻混沌电路模型, 研究了偏置电压对其系统动态行为的影响. 再次, 在PSpice中搭建了分数阶的等效电路模型, 并对其进行电路仿真验证, 实验结果与数值仿真基本一致. 最后, 在LabVIEW中完成了电路实验, 验证了理论分析的正确性与可行性. 结果表明, 含有偏置电压源的分数阶忆阻器, 可以通过调控偏置电压源的电压, 连续获得不对称紧磁滞回线. 随着偏置电源电压的改变, 非齐次分数阶忆阻混沌系统由于对称性的破环, 表现出由倍周期分岔进入混沌的行为.A physical memristor has an asymmetric tight hysteresis loop. In order to simulate the asymmetric tight hysteresis curve of the physical memristor more conveniently, a fractional-order diode bridge memristor model with a bias voltage source is proposed in this paper, which can continuously regulate the hysteresis loop. Firstly, based on fractional calculus theory, a fractional order model of a diode bridge memristor with a bias voltage source is established, and its electrical characteristics are analyzed. Secondly, by integrating it with the Jerk chaotic circuit, a non-homogeneous fractional order memristor chaotic circuit model with a bias voltage source is established, and the influence of bias voltage on its system dynamic behavior is studied. Once again, a fractional-order equivalent circuit model is built in PSpice and validated through circuit simulation. The experimental results are basically consistent with the numerical simulation results. Finally, the experiments on the circuit are completed in LabVIEW to validate the correctness and feasibility of the theoretical analysis. The results indicate that the fractional order memristor with bias voltage source can continuously obtain asymmetric tight hysteresis loop by adjusting the voltage of the bias voltage source. As the bias power supply voltage changes, the non-homogeneous fractional order memristor chaotic system exhibits that the period doubling bifurcation turns into chaos due to the symmetry breaking.
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Keywords:
- memristor/
- chaotic circuit/
- fractional calculus/
- circuit experiment
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d值 平衡点 特征值λ1—λ4 稳定性 0, 0.1, 0.3 P0(0, 0, 0, 0) 0.3773, –0.6886 ±5.2293i, –0.0172 指数–1 USF 0, 0.1, 0.3 P–(–19.7558, 0, 0, 1.9755) 1.2573 ±5.8895i, –3.5516, –0.0143 指数–2 USF 0 P+(19.7558, 0, 0, 1.9755) 1.2573 ±5.8895i, –3.5516, –0.0143 指数–2 USF 0.1 P+(19.9495, 0, 0, 1.9949) 1.2689 ±5.8991i, –3.5751, –0.0143 指数–2 USF 0.3 P+(20.3363, 0, 0, 2.0336) 1.2918 ±5.9182i, –3.6215, –0.0143 指数–2 USF 
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Rin/Ω Ro1/Ω Ro2/(103Ω) Ro3/(105Ω) Ro4/(109Ω) Ro5/(105Ω) $C_{\text{m}}^{{q_1}} = 5.8 \times {10^3}{\text{ nF}}$ 0.2273 5.327 1.203 2.705 1.158 1.209 $C_{2}^{{q_2}} = 10{\text{ nF}}$ 114.8 1461 348.7 828.9 730.0 837.3 下载:
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Co1/(10–7F) Co2/(10–7F) Co3/(10–7F) Co4/(10–8F) Co1/(10–5F) $C_{\text{m}}^{{q_1}} = 5.8 \times {10^3}{\text{ nF}}$ 446.2 496.3 554.3 647.8 6200 $C_{2}^{{q_2}} = 10{\text{ nF}}$ 1.672 1.760 1.860 1.057 9.214 下载:
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