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Bistable chaotic family and its chaotic mechanism

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  • Cheng, Guanghui
  • Gui, Rong

Abstract

The emergence of many chaotic families shows that chaos can be generated by deterministic approaches. From the perspective of the mechanism of chaos, we add the opposite time-delayed effects to an overdamped bistable system to obtain chaos. The effect of time delay is determined by the change of the optimal window which origin from logical stochastic resonance. A variety of chaotic systems with different chaotic attractors are obtained by different combinations of opposite effects. Furthermore, we propose the mechanism of chaos in time-delayed bistable systems, that is, the opposite time-delayed effects lead to repeated increasing and decreasing in depth of potential wells. This mechanism is verified by constructing a force-free Duffing equation with an oscillatory double-well potential. Results show that the bistable systems can form bistable chaotic family based on the same chaos generation mechanism.

Suggested Citation

  • Cheng, Guanghui & Gui, Rong, 2022. "Bistable chaotic family and its chaotic mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    • Handle: RePEc:eee:chsofr:v:162:y:2022:i:c:s0960077922006178
    DOI: 10.1016/j.chaos.2022.112407
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    Cited by:

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    4. Wang, Xueqin & Yu, Dong & Li, Tianyu & Jia, Ya, 2023. "Logistic stochastic resonance in the Hodgkin–Huxley neuronal system under electromagnetic induction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).

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