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Coexisting infinitely many attractors in active band-pass filter-based memristive circuit

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Abstract

This paper presents an inductor-free memristive circuit, which is implemented by linearly coupling an active band-pass filter (BPF) with a parallel memristor and capacitor filter. Mathematical model is established, and numerical simulations are performed. The results verified by hardware experiments show that the active BPF-based memristive circuit exhibits the dynamical behaviors of point, period, chaos, and period-doubling bifurcation route. Most important of all, the newly proposed memristive circuit has a line equilibrium and its stability closely relies on memristor initial condition, which results in the emergence of extreme multistability. Stability distribution related to memristor initial condition is numerically estimated and the coexistence of infinitely many attractors is intuitively captured by numerical simulations and PSIM circuit simulations.

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Acknowledgments

This work was supported by the grants from the National Natural Science Foundations of China (Grant No. 51277017), the Scientific Research Foundation of Jiangsu Provincial Education Department, China under Grant Nos. 14JKB430004 and 15KJB510001, and the Natural Science Foundations of Changzhou, Jiangsu Province, China (Grant No. CJ20159026).

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Authors and Affiliations

  1. Department of Electrical Engineering and Electronics, University of Liverpool, Brownlow Hill, Liverpool, L69 3GJ, UK

    Yihua Hu

  2. School of Information Science and Engineering, Changzhou University, Changzhou, 213164, China

    Bocheng Bao, Tao Jiang, Quan Xu, Mo Chen & Huagan Wu

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  1. Bocheng Bao
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Correspondence to Yihua Hu.

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Bao, B., Jiang, T., Xu, Q. et al. Coexisting infinitely many attractors in active band-pass filter-based memristive circuit. Nonlinear Dyn 86, 1711–1723 (2016). https://doi.org/10.1007/s11071-016-2988-6

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