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A symmetric oscillator with multi-stability and chaotic dynamics: bifurcations, circuit implementation, and impulsive control

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Abstract

Finding chaotic oscillators with unique properties is a hot topic. In this paper, a symmetric oscillator with multi-stability is proposed. This oscillator has bounded dynamics for any initial conditions. It is also shown that the oscillator has one unstable equilibrium. This paper studies the dynamical properties of the oscillator, such as chaotic attractors, Lyapunov exponents (LEs), bifurcation diagrams, and the basin of attraction. Its feasibility is shown by circuit implementation. In addition, the stabilization of the system is investigated by impulsive control.

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Acknowledgements

This work is partially supported by the Natural Science Basic Research Program of Shaanxi (2021JM-533, 2021JQ-880, 2020JM-646), the Innovation Capability Support Program of Shaanxi (2018GHJD-21), the Science and Technology Program of Xi’an (2019218414GXRC020CG021-GXYD20.3), the Support Plan for Sanqin Scholars Innovation Team in Shaanxi Province of China and the Scientific Research Fund for High-Level Talents of Xijing University (XJ21B01). This work is partially funded by Centre for Nonlinear Systems, Chennai Institute of Technology, India vide funding number CIT/CNS/2021/RD/064.

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Authors and Affiliations

  1. School of Science, Xijing University, Xi’an, 710123, People’s Republic of China

    Zhen Wang, Min Zhang & Rui Yang

  2. Centre for Additive Manufacturing, Chennai Institute of Technology, Chennai, India

    Dhinakaran Veeman

  3. Information Technology Collage, Imam Ja’afar Al-Sadiq University, 10001, Baghdad, Iraq

    Hayder Natiq

  4. Mathematics Program, Department of Mathematics, Statistics and Physics, College of Arts and Sciences, Qatar University, 2713, Doha, Qatar

    Iqtadar Hussain

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  1. Zhen Wang
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Wang, Z., Veeman, D., Zhang, M. et al. A symmetric oscillator with multi-stability and chaotic dynamics: bifurcations, circuit implementation, and impulsive control. Eur. Phys. J. Spec. Top. 231, 2153–2161 (2022). https://doi.org/10.1140/epjs/s11734-021-00371-y

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