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Understanding Chua system from the perspective of Duffing

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  • Cheng, Guanghui
  • Gui, Rong

Abstract

The generation methods and structure of the multi-scroll chaotic attractors in both the Chua system and the Duffing equation exhibit remarkable similarities, suggesting a potential relationship between these two systems. Specifically, the Chua system can be transformed into a Duffing-like equation. In this transformation, the second equation of the Chua system forms the main body of the Duffing equation, while the first and third equations contribute to forming potential wells. Consequently, parameters in the Chua system possess physical meanings corresponding to those in the Duffing equation, enabling us to control the Chua system as if it is a Duffing equation. By adjusting various factors such as damping coefficient, potential difference among potential wells, the shape of the potential wells, asymmetric bias, external driving force and oscillation characteristics of potential wells within Chua system framework, we can successfully obtain controllable multi-scroll chaotic attractors. The Multisim simulation circuit and analog circuit experiments have confirmed the results.

Suggested Citation

  • Cheng, Guanghui & Gui, Rong, 2024. "Understanding Chua system from the perspective of Duffing," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    • Handle: RePEc:eee:chsofr:v:185:y:2024:i:c:s0960077924007045
    DOI: 10.1016/j.chaos.2024.115152
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