Nonlinear Dynamics

, Volume 95, Issue 2, pp 1245–1256 | Cite as

Conditional symmetry: bond for attractor growing

  • Chunbiao LiEmail author
  • Yujie Xu
  • Guanrong Chen
  • Yongjian Liu
  • Jincun Zheng
Original Paper


Coexisting attractors with conditional symmetry exist in separated asymmetric basins of attraction with identical Lyapunov exponents. It is found that when a periodic function is introduced into the offset-boostable variable, infinitely many coexisting attractors may be coined. More interestingly, such coexisting attractors may be hinged together and then grow in the phase space as the time evolves without any change of the Lyapunov exponents. It is shown that, in such cases, an initial condition can be applied for selecting the starting position; consequently, the system will present a special regime of homogenous multistability. Circuit implementation based on STM32 verifies the numerical simulations and theoretical analysis.


Conditional symmetry Homogenous multistability Attractor Offset boosting 



Chunbiao Li was supported by the National Nature Science Foundation of China (Grant No.: 61871230), the Natural Science Foundation of Jiangsu Province (Grant No.: BK20181410), the Startup Foundation for Introducing Talent of NUIST (Grant No.: 2016205) and a Project Funded by the Priority Academic Program Development of the Jiangsu Higher Education Institutions, Yongjian Liu was supported by the National Natural Science Foundation of China (Grant No.: 11561069). The authors thank Lijiang Dong for his help with STM32 implementation.

Compliance with ethical standards

Conflict of Interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  • Chunbiao Li
    • 1
    • 2
    Email author
  • Yujie Xu
    • 1
    • 2
  • Guanrong Chen
    • 3
  • Yongjian Liu
    • 4
  • Jincun Zheng
    • 4
  1. 1.Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CICAEET)Nanjing University of Information Science and TechnologyNanjingChina
  2. 2.Jiangsu Key Laboratory of Meteorological Observation and Information ProcessingNanjing University of Information Science and TechnologyNanjingChina
  3. 3.Department of Electronic EngineeringCity University of Hong KongKowloonChina
  4. 4.Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data ProcessingYulin Normal UniversityYulinChina

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