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A Unique Jerk System with Abundant Dynamics: Symmetric or Asymmetric Bistability, Tristability, and Coexisting Bubbles

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Abstract

Finding and revealing new features and behaviors of simple chaotic systems have always been an important and attractive research topic. This paper aims to introduce a new 3D autonomous jerk chaotic system and explore its rich dynamical behaviors including period-doubling bifurcation and reverse period-doubling bifurcation routes to chaos, crisis and internal crisis, multiple symmetric coexisting attractors, and antimonotonicity. Especially, the phenomena of asymmetric bistability (e.g., coexistence of a point attractor and chaotic attractor or coexistence of a point attractor and period-5 limit cycle), tristability (e.g., coexistence of a point attractor and a pair of symmetric chaotic or periodic attractors), and coexisting bubbles are found, which have been rarely reported before. By using standard nonlinear analysis methods such as bifurcation diagrams, the largest Lyapunov exponent, phase portraits, Poincaré sections, 0–1 test chart and the basin of attraction for an attractor, and the complex dynamical behaviors of the system are investigated in detail. Furthermore, a corresponding hardware electronic circuit is designed to verify the numerical simulations.

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Funding

The work was supported by the National Natural Science Foundations of China under Grant No. 61471310.

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  1. School of Physics and Optoelectric Engineering, Xiangtan University, Xiangtan, 411105, Hunan, China

    Ying Li, Yicheng Zeng & Jingfang Zeng

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  1. Ying Li
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Correspondence to Yicheng Zeng.

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Li, Y., Zeng, Y. & Zeng, J. A Unique Jerk System with Abundant Dynamics: Symmetric or Asymmetric Bistability, Tristability, and Coexisting Bubbles. Braz J Phys 50, 153–163 (2020). https://doi.org/10.1007/s13538-019-00731-z

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