Hidden Attractors in a Delayed Memristive Differential System with Fractional Order and Chaos Synchronization  

作　　者：Dawei Ding Yecui Weng Nian Wang 

机构地区：[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

出　　处：《Journal of Harbin Institute of Technology(New Series)》2020年第1期67-75,共9页哈尔滨工业大学学报（英文版）

基　　金：Sponsored by the National Natural Science Foundation of China(Grant No.61201227);the Funding of China Scholarship Council,the Natural Science the Foundation of Anhui Province(Grant No.1208085M F93);the 211 Innovation Team of Anhui University(Grant Nos.KJTD007A and KJTD001B)

摘　　要：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 delayτon chaos synchronization.The simulation results confirm that the chaotic synchronization is affected by a,q andτ.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.

关 键 词：fractional order memristive time⁃delay hidden attractors chaos synchronization 

分 类 号：N93[自然科学总论]