Design and Implementation of Memristor-based Chaotic Synchronization under a Single Input Controller
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摘要: 该文提出一种在单输入控制器下基于忆阻器的混沌同步模拟电路设计及其实现方法，并将它应用于基于忆阻混沌同步的保密通信。首先，基于混沌同步理论，构建了混沌同步系统及保密通信模型，并设计实现了一种4阶压控忆阻混沌电路和混沌加密解密电路。其次，将所设计的忆阻混沌电路作为混沌驱动和响应电路，根据它们的误差系统设计了一种单输入混沌同步控制器，并将其实现于忆阻混沌同步电路当中。最后，完成了基于忆阻混沌同步的保密通信电路实验。实验结果表明，所设计忆阻混沌同步电路结构简单、操作方便、波形良好，在单输入控制器下电路能够快速同步并保持稳定，且在保密通信实验中信号还原度高、受损程度小、抗破译能力强，具有一定的理论意义与潜在的实用价值。Abstract: A memristor-based chaotic synchronization circuit is designed and implemented under a single-input controller, and it is applied to secure communication based on memristor chaotic synchronization. Firstly, based on the chaotic synchronization theory, a chaotic synchronization system and secure communication model are constructed, and a fourth-order memristor-based chaotic circuit is implemented, the chaotic en-/decryption circuit is also designed. Secondly, the proposed memristor-based chaotic circuit is considered as the chaotic drive and response circuits, and a single-input chaotic synchronization controller is designed according to their error system, and it is implemented in the memristor-based chaotic synchronization circuit. Finally, many experiments of chaotic synchronization and secure communication based on chaotic synchronization are performed, and experimental results show that the proposed memristor-based chaotic synchronization circuit has many advantages, such as simple structure, convenient operation and good waveform. Furthermore, secure communication based on chaotic synchronization has high signal recovery capability and good anti-decipher ability, so that it has certain theoretical significance and potential practical value.
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Key words:
- Chaotic synchronous circuit /
- Memristor /
- Controller /
- Secure communication
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表 1 系统参数
参数 $ \alpha $ $ \beta $ $ \chi $ $ \delta $ $ \varepsilon $ $ \gamma $ 表达式 $ \dfrac{1}{{{R_9}{C_1}}} $ $ \dfrac{1}{{{R_5}{C_1}}} $ $ \dfrac{{{R_6}}}{{{R_7}{R_8}{C_1}}} $ $ \dfrac{1}{{{R_9}{C_2}}} $ $ \dfrac{1}{{{C_2}}} $ $ \dfrac{1}{{{R_1}{C_3}}} $ 
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表 2 基于忆阻混沌同步的保密通信电路参数取值
参数 参值 参数 参值 参数 参值 参数 参值 $ {R_1} $,$ {R_{13}} $ 8.2 kΩ $ {R_2} $,$ {R_{14}} $ 1.5 kΩ $ {R_3} $,$ {R_4} $,$ {R_{15}} $,$ {R_{16}} $ 2 kΩ $ {R_5} $,$ {R_{17}} $ 264 Ω $ {R_6} $,$ {R_7} $,$ {R_{18}} $,$ {R_{19}} $ 500 Ω $ {R_8} $,$ {R_{20}} $,$ {R_{28}} $,$ {R_{29}} $ 1 kΩ $ {R_9} $,$ {R_{21}} $,$ {R_{46}} $ 2.14 kΩ $ {R_{10}} $,$ {R_{24}} $ 39 kΩ $ {R_{11}} $,$ {R_{23}} $ 15 kΩ $ {R_{12}} $,$ {R_{22}} $ 11 kΩ $ {R_{25}} $,$ {R_{26}} $ 27 kΩ $ {R_{27}} $ 43 kΩ $ {R_{30}} $,$ {R_{31}} $,$ {R_{32}} $,$ {R_{33}} $ 10 kΩ $ {R_{34}} $,$ {R_{36}} $,$ {R_{41}} $,$ {R_{43}} $ 10 kΩ $ {R_{35}} $,$ {R_{37}} $,$ {R_{38}} $,$ {R_{40}} $ 18 kΩ $ {R_{39}} $,$ {R_{44}} $ 12.62 kΩ $ {R_{45}} $ 18 kΩ $ {C_1} $,$ {C_4} $,$ {C_5} $,$ {C_8} $ 68 nF $ {C_2} $,$ {C_6} $ 6.8 nF $ {C_3} $,$ {C_7} $ 47 nF $ {C_9} $ 10 nF $ {C_{10}} $ 2.2 nF
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表 3 同步后各状态变量的误差信号统计
参数 最大值（V） 最小值（V） Matlab仿真 $ {e_1} $ 0.0003 –0.0002 $ {e_2} $ 0.0005 –0.0004 $ {e_3} $ 0.0012 –0.0008 $ {e_4} $ 0.0004 –0.0001 电路仿真 $ {e_1} $ 0.1070 –0.0610 $ {e_2} $ 0.0850 –0.0450 $ {e_3} $ 0.2410 –0.0970 $ {e_4} $ 0.0940 –0.0380 实际电路 $ {e_1} $ 0.4450 –0.2680 $ {e_2} $ 0.5910 –0.2840 $ {e_3} $ 0.6120 –0.5590 $ {e_4} $ 0.4830 –0.2570
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