Bursting, Coexistence Analysis and DSP Implementation of Duffing System Based on Hyperbolic-tangent Memristor
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摘要: 忆阻器作为第4种基本电路元件由蔡少棠首次提出，它的提出为混沌电路的设计和工程应用提供了新思路。该文通过在Homles型Duffing系统中引入一个双曲正切忆阻模型，得到了一个新忆阻Duffing非自治系统。利用转换相图、相图、Lyapunov指数等，揭示了该系统具有振荡尖峰数目可控簇发、非完全对称双边簇发、非完全对称的簇发共存、多种周期混沌共存等新颖动力学行为。并通过分岔图及平衡点分析，研究了其簇发产生机理。采用Multisim电路仿真与数字信号处理平台(DSP)对系统进行了硬件实现，与理论分析基本一致的实验结果证明该系统是可行的且是物理可实现的。Abstract: Memristor is first proposed by Chua as the fourth basic circuit element, which provides a novel idea for the design and engineering application of chaotic circuits. A novel memristive Duffing nonautonomous system is obtained by introducing a hyperbolic-tangent memristor into the Homles type Duffing system. By using the transformed phase portraits, phase portraits, Lyapunov exponents, etc., it is revealed that the system has novel dynamical behaviors such as bursts with controllable number of oscillation spikes, non-completely symmetrical bilateral bursts, coexistence of non-completely symmetrical bursts, multiple coexistence of chaos and period. The mechanism of bursting is studied by analysis of equilibrium point and bifurcation diagram. Multisim circuit simulation and Digital Signal Processing platform (DSP) are used to implement the system in hardware, and the experimental results basically consistent with the theoretical analysis prove that the system is feasible and physically achievable.
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Key words:
- Memristor /
- Duffing /
- Bursting /
- Delayed bifurcation /
- Coexistence
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