| Author Name | Affiliation | | Dawei Ding | School of Electronics and Information Engineering, Anhui University, Hefei 230601, China
Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, Anhui University, Hefei 230601, China | | Yecui Weng | School of Electronics and Information Engineering, Anhui University, Hefei 230601, China
Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, Anhui University, Hefei 230601, China | | Nian Wang | School of Electronics and Information Engineering, Anhui University, Hefei 230601, China
Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, Anhui University, Hefei 230601, China |
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| Abstract: |
| As an important research branch, memristor has attracted a range of scholars to study the property of memristive chaotic systems. Additionally, time-delayed systems are considered a significant and newly-developing field in modern research. By combining memristor and time-delay, a delayed memristive differential system with fractional order is proposed in this paper, which can generate hidden attractors. First, we discussed the dynamics of the proposed system where the parameter was set as the bifurcation parameter, and showed that with the increase of the parameter, the system generated rich chaotic phenomena such as bifurcation, chaos, and hypherchaos. Then we derived adequate and appropriate stability criteria to guarantee the system to achieve synchronization. Lastly, examples were provided to analyze and confirm the influence of parameter a, fractional order q, and time delay τ on chaos synchronization.The simulation results confirm that the chaotic synchronization is affected by a,q and τ . |
| Key words: fractional order memristive time-delay hidden attractors chaos synchronization |
| DOI：10.11916/j.issn.1005-9113.18108 |
| Clc Number:N93 |
| Fund: |
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| Descriptions in Chinese: |
| 分数阶时滞忆阻差分系统的隐藏吸引子和混沌同步 丁大为1，2，翁业翠1，2，王年1，2 （1.安徽大学 电子与信息工程学院，合肥230601； 2.安徽大学 教育部智能计算与信号处理重点实验室，合肥230601） 创新点说明：1）结合忆阻器和时滞，提出一种具有隐藏吸引子的新型分数阶延迟忆阻差分系统。根据系统的分岔图，观察了所提出的系统随参数变化的演化规律，发现该系统比对应的整数阶物具有更复杂的混沌行为。 2）研究系统的同步，设计简单的控制方法，得到误差方程，通过讨论和分析具有零个根的误差系统的稳定性，可实现驱动系统（8）和响应系统（10）之间的同步。其中控制方法既简单又可行。 3）将系数参数a、分数阶数、时滞作为分岔参数，给出具体数值，研究和讨论其对混沌同步的影响。 研究目的： 研究一个具有时滞的分数阶忆阻差分系统的动力学行为，推导其实现同步状态的必要条件，并进一步讨论了关于影响同步状态的因素（如差分系统的系数a，分数阶数，时滞），通过数值仿真证明所研究的结果。 研究方法： 给出时域图、相图、分岔图等研究差分系统的动力学行为。对于系统的同步，设计简单的控制方法，得到误差方程，接着对误差方程进行稳定性分析，推导出稳定条件，结合Matlab软件，给出同步状态图，误差系统的图。 结果和结论： 软件数值结果与其推导结果一致。将差分系统的系数参数、分数阶数、时滞作为分岔参数，发现其确实影响着混沌同步状态。即： 1）参数a对同步的影响。随着系数a增加，误差函数e1的同步状态变慢； 由于系统（14）的误差函数e2与参数a无关，因此同步状态随着参数a增加而保持不变。 2）分数阶数对同步的影响。分数阶数增加的越快，误差系统e1趋向于同步越慢，而误差系统e2趋向于同步越快。 3）时滞对同步的影响。时滞增加的越快，误差系统e1趋向于同步越快，而由于系统（14）的误差函数e2与时滞无关，则误差系统e2不变化。 关键词：分数阶;忆阻;时滞; 隐藏的吸引子;混沌同步 |
