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Multistability induced by two symmetric stable node-foci in modified canonical Chua’s circuit

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Abstract

This paper proposes a modified canonical Chua’s circuit using an one-stage op-amp-based negative impedance converter and an anti-parallel diode pair. Unlike the conventional Chua’s circuit, this modified canonical Chua’s circuit has one unstable zero node-focus and two stable nonzero node-foci, but complex dynamical behaviors including period, chaos, stable point, and coexisting bifurcation modes are numerically revealed and experimentally verified. Up to six kinds of coexisting multiple attractors, i.e., left-right limit cycles, left-right chaotic spiral attractors and left-right point attractors, are numerically depicted and physically captured. Furthermore, with dimensionless Chua’s equations, dynamical properties of the Chua’s system are investigated, and two symmetric stable nonzero node-foci are validated to exist in the selected parameter regions thus resulting in the emergence of multistability. Specially, multistability with six different steady states is revealed in a narrow parameter range. Within this parameter region, three bifurcation routes are displayed under different initial conditions, and three sets of topologically different and disconnected attractors are observed.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant Nos. 51277017 and 61601062, the Natural Science Foundation of Jiangsu Province, China under Grant No. BK20160282, and the Scientific Research Foundation of Jiangsu Provincial Education Department, China under Grant No. 15KJB510001.

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  1. School of Information Science and Engineering, Changzhou University, Changzhou, 213164, People’s Republic of China

    Mo Chen, Quan Xu, Yi Lin & Bocheng Bao

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  1. Mo Chen
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Correspondence to Bocheng Bao.

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Chen, M., Xu, Q., Lin, Y. et al. Multistability induced by two symmetric stable node-foci in modified canonical Chua’s circuit. Nonlinear Dyn 87, 789–802 (2017). https://doi.org/10.1007/s11071-016-3077-6

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