Hidden extreme multistability generated from a fractional-order chaotic system

  • Xiang Li
  • Zhijun LiEmail author
Original Paper


A new 4D fractional-order chaotic system with no equilibrium is proposed in this paper. One salient feature of this system is that it has no equilibrium point, which leads to the lack of homo-clinic or hetero-clinic trajectory. Thus, Shil’nikov theorem is not suitable to prove the existence of chaos in this system. However, the system can exhibit complex dynamic behaviors when its system parameter and fractional derivative order are varied. More interesting, the dynamics depending on initial values are also investigated and a more complex phenomenon of hidden extreme multistability is revealed. Furthermore, by selecting the appropriate system parameters, the state transition behaviors can be also found in this system. Finally, in order to verify the feasibility of the proposed fractional-order chaotic system, the corresponding physical circuit is designed by using the modular design method. The hardware experimental results are in good agreement with numerical analysis.


Chaos Fractional dynamics Hidden extreme multistability State transition behavior Circuit implementation 


05.45.-a 05.45.Df 05.45.Pq 



The authors would like to thank the National Natural Science Foundation of China (Grant Nos. 61176032 and 61471310) and the Natural Science Foundation of Hunan Province, China (Grant No. 2015JJ2142), for supporting this research.


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Copyright information

© Indian Association for the Cultivation of Science 2019

Authors and Affiliations

  1. 1.College of Information EngineeringXiangtan UniversityXiangtanChina

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