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Supervised by Ministry of Industry and Information Technology of The People''s Republic of China Sponsored by Harbin Institute of Technology Editor-in-chief Yu Zhou ISSNISSN 1005-9113 CNCN 23-1378/T

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Hidden Attractors in a Delayed Memristive Differential System with Fractional Order and Chaos Synchronization
Dawei Ding1,2, Yecui Weng1,2, Nian Wang1,2
1. School of Electronics and Information Engineering, Anhui University, Hefei 230601, China;2. Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, Anhui University, Hefei 230601, China
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:
Descriptions in Chinese:
  忆阻器作为一个重要的研究分支,吸引了一系列学者关注忆阻混沌系统的性质研究。时滞系统被认为是现代研究中一个非常重要和新兴的领域。结合忆阻器和时滞,提出了一种具有分数阶的延迟忆阻差分系统,它可以产生隐藏的吸引子。最初,我们讨论了所提出系统的动力学,其中参数a被设置为分岔参数,研究表明随着参数a的增加,该系统产生丰富的混沌现象,例如分岔,混沌,超混沌。之后通过一些充分和适当的稳定性判据推导出来,以保证这种混沌系统实现同步。通过提供一些例子来讨论参数a,分数阶q和时滞τ是否对混沌同步有影响。最后,得到的仿真结果证实了参数a,分数阶q和时滞τ确实影响着混沌同步。

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