| Related citation: | Dawei Ding,Hui Liu,Yecui Weng,Xiaolei Yao,Nian Wang.Dynamics Analysis of Fractional-Order Memristive Time-Delay Chaotic System and Circuit Implementation[J].Journal of Harbin Institute Of Technology(New Series),2020,27(2):65-74.DOI:10.11916/j.issn.1005-9113.18084. |
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| Author Name | Affiliation | | Dawei Ding | School of Electronics and Information Engineering, Anhui University, Hefei 230601, China | | Hui Liu | School of Electronics and Information Engineering, Anhui University, Hefei 230601, China | | Yecui Weng | School of Electronics and Information Engineering, Anhui University, Hefei 230601, China | | Xiaolei Yao | School of Electronics and Information Engineering, Anhui University, Hefei 230601, China | | Nian Wang | School of Electronics and Information Engineering, Anhui University, Hefei 230601, China |
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| Abstract: |
| The integer-order memristive time-delay chaotic system has attracted much attention and has been well discussed. However, the fractional-order system is closer to the real system. In this paper, a nonlinear time-delay chaotic circuit based on fractional-order memristive system was proposed. Some dynamical properties, including equilibrium points, stability, bifurcation, and Lyapunov exponent of the oscillator, were investigated in detail by theoretical analyses and simulations. Moreover, the nonlinear phenomena of coexisting bifurcation and attractor was found. The phenomenon shows that the state of this oscilator was highly sensitive to its initial value, which is called coexistent oscillation in this paper. Finally, the results of the system circuit simulation accomplished by Multisim were perfectly consistent with theoretical analyses and numerical simulation. |
| Key words: fractional-order time-delay coexisting attractors coexisting bifurcation circuit simulation |
| DOI：10.11916/j.issn.1005-9113.18084 |
| Clc Number:O415.5 |
| Fund: |
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| Descriptions in Chinese: |
| 基于分数阶忆阻器的时延混沌系统动力学分析和电路仿真 丁大为，刘慧，翁业翠，姚晓磊，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器的时延混沌系统。分析了分数阶忆阻器的频率和电特性。研究了实现分数阶忆阻器的单元电路。首先，根据李亚普诺夫间接法，对分数阶忆阻器的时延混沌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，根据改变系统参数，得到不同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。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。本文还研究了共存分叉和共存吸引子的非线性现象。该现象表明该振荡器的状态对其初始值非常敏感，本文称之为共存振荡。此外，使用改进的Adams-Bashforth-Moulton方法研究数值模拟。最后，对该时滞混沌电路进行电路仿真，与理论分析和数值模拟的结果一致。 关键词：分数阶；时延；共存吸引子；共存分岔；电路仿真 |
