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| Abstract: |
| For the purpose of investigating the nonlinear dynamics of the system, a fractional-order Chuaｓ circuit based on the memristor deriving from the integer-order counterparts is provided. Firstly, according to the Lyapunovｓ indirect method, the stability analysis of the memristive system is made, and it shows that when the fractional-orders parameter of memristive system passes a critical value, the system loses the stability and bifurcation occurs. Then the bifurcation and chaos behaviors of fractional-order memristive system are shown using bifurcation diagrams with varying fractional orders of the system and other parameters. Furthermore, the chaotic behaviors of memristive chaotic system are proved by the waveform, phase plot and largest Lyapunov exponent diagram. Finally, theoretical results are illustrated and validated with the given numerical simulations. |
| Key words: memristor dynamical behavior fractional-order stability |
| DOI：10.11916/j.issn.1005-9113.16136 |
| Clc Number:O415.5 |
| Document Code::A |
| Fund: |
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| Descriptions in Chinese: |
| 分数阶忆阻器混沌电路的动力学分析 丁大为，李书家，王年 (安徽大学 电子信息工程学院，合肥 230601) 中文说明：为研究系统的非线性动力学，提出一个从相对应的整数阶演变而来的分数阶忆阻蔡氏电路。首先，根据李亚普诺夫间接法，对分数阶忆阻系统的稳定性进行分析，结果表明：当忆阻系统的分数阶参数达到临界值时，系统失去稳定性，并发生分岔。然后，根据不同分数阶阶数以及不同其他系统参数的分岔图表明分数阶忆阻系统发生分岔和混沌行为。此外，为证明分数阶忆阻混沌系统存在混沌行为，给出了系统的时域图、相位图和最大的李亚普诺夫指数图。最后，通过数值仿真说明和验证理论结果的正确性。 关键词：忆阻器；动力学行为；分数阶；稳定性 |
