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Conditional symmetry: bond for attractor growing

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Abstract

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.

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Acknowledgements

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.

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Authors and Affiliations

  1. Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CICAEET), Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Chunbiao Li & Yujie Xu

  2. Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Chunbiao Li & Yujie Xu

  3. Department of Electronic Engineering, City University of Hong Kong, Kowloon, 999077, Hong Kong SAR, China

    Guanrong Chen

  4. Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin, 537000, Guangxi, China

    Yongjian Liu & Jincun Zheng

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  1. Chunbiao Li
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  2. Yujie Xu
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  3. Guanrong Chen
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Correspondence to Chunbiao Li.

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Li, C., Xu, Y., Chen, G. et al. Conditional symmetry: bond for attractor growing. Nonlinear Dyn 95, 1245–1256 (2019). https://doi.org/10.1007/s11071-018-4626-y

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  • DOI: https://doi.org/10.1007/s11071-018-4626-y

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