A Simple Inductor-free Memristive Chaotic Circuit and Its Characteristics
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摘要: 采用非理想有源电压控制忆阻器和磁通控制型光滑3次非线性忆阻器，该文设计了一种不含电感的简单(只含5个电子元器件)双忆阻混沌电路。采用常规的非线性分析手段详细研究了电路参数变化时系统的基本动力学行为，例如平衡点稳定性分析，相轨图以及李雅普诺夫指数谱和分岔图等。通过调节系统控制参数，该系统可产生多涡卷、多翼以及暂态混沌等十分丰富的动力学现象。此外，还研究了系统依赖于忆阻器初始状态的多稳态，得到了一些有意义的结果。为验证电路的可行性及稳定性，通过对忆阻器的模拟等效电路的搭建，并将该等效电路应用于所提出的混沌电路中，硬件电路实验结果以及Multisim电路仿真结果与理论分析一致。Abstract: A simple two-memristor chaotic circuit without inductance (only five electronic components) is designed by using a non-ideal active voltage control memristor and a flux-controlled smooth cubic nonlinear memristor. When the circuit parameters change, the basic dynamic behaviors of the system are studied in detail by the means of conventional nonlinear analysis, such as the analysis of equilibrium stability, phase diagram, Lyapunov exponent spectrum and bifurcation diagram. With the parameters changing, the proposed system can produce various phenomena of dynamics such as multi-scrolls, multi-wings and transient transition behaviors. Furthermore, the multistability characteristics of the system are also studied in the condition of changing the initial state of two memristors in system respectively, and some meaningful results are obtained. In order to verify the feasibility and stability of the circuit, the analog equivalent circuit of each memristor is constructed, and it is applied to the proposed chaotic circuit. The experimental results of the hardware circuit and the circuit simulation results of the Multisim are in good agreement with the theoretical analysis.
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Key words:
- Memristor /
- Chaotic circuit /
- Multistability /
- Transient transition behaviors
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表 1 忆阻器W3随初始状态变化所产生的多稳态举例
z(0)取值 LE李雅普诺夫指数 系统状态 4.0 (+, 0, –, –) 2翼混沌吸引子 6.5 (+, 0, –, –) 4翼混沌吸引子 13.5 (+, 0, –, –) 6翼混沌吸引子 17.5 (+, 0, –, –) 8翼混沌吸引子 
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表 2 简洁无电感忆阻混沌电路的参数取值
参数 名称 参值 $ {C_a},{C_1},{C_3}$ 电容 1 nF C2 电容 25 nF $ {g_a},{\rm{ }}{g_b},{\rm{ }}{g_{3,}}{g_4}$ 增益 1 $ {g_1},{\rm{ }}{g_2}$ 增益 0.1 R1 电阻 0.25 kΩ R2 电阻 50.00 kΩ R3 电阻 25.00 kΩ $ {R_4},{\rm{ }}{R_c}$ 电阻 10.00 kΩ Rb 电阻 16.70 kΩ $ {R_d},{R_e}_,{R_5}{,}{R_6}$ 电阻 2.00 kΩ
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