A novel amplitude control method for constructing nested hidden multi-butterfly and multiscroll chaotic attractors

Qiujie Wu, Qinghui Hong, Xiaoyang Liu, Xiaoping Wang and Zhigang Zeng

Chaos, Solitons & Fractals, 2020, vol. 134, issue C

Abstract: A novel amplitude control method (ACM) is proposed to construct multiple self-excited or hidden attractors by scaling partial or total variables without changing their dynamic and topological properties. Various attractors including nested attractor, axisymmetric attractor, and centrosymmetric attractor can be obtained by multiplying signals with different amplitudes. An universal pulse control module is designed to realize the amplitude scale. Different number of scrolls can be adjusted by regulating the pulse signals without redesigning the nonlinear circuit. The classical Lorenz system and Jerk system are employed as examples to generate nested hidden multi-butterfly and multiscroll attractors. Some novel properties of ACM, such as nested morphology, amplitude modulation, and constant Lyapunov exponential spectrum, are analyzed theoretically and simulated numerically. The circuit design and PSpice simulation results are implemented to verify the availability and feasibility of the proposed approach.

Keywords: Amplitude control; Nested chaotic attractor; Constant Lyapunov exponents; Hidden attractor (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:134:y:2020:i:c:s0960077920301296

DOI: 10.1016/j.chaos.2020.109727

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