Comprehensive analysis of the mechanism of sensitivity to initial conditions and fractal basins of attraction in a novel variable-distance magnetic pendulum

Qin, Bo; Zhang, Ying

doi:10.1016/j.chaos.2024.114933

Chaos, Solitons & Fractals

2024

DOI: 10.1016/j.chaos.2024.114933

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Comprehensive analysis of the mechanism of sensitivity to initial conditions and fractal basins of attraction in a novel variable-distance magnetic pendulum

Bo Qin,

Ying Zhang

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Cited by 4 publications

References 44 publications

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Dynamic analysis of a class of fractional‐order dry friction oscillators

Si,

Xie,

Zhao

et al. 2024

Math Methods in App Sciences

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This article investigates a class of Duffing nonlinear dynamic systems with fractional‐order dry friction and conducts in‐depth research on the stability, chaotic characteristics, and erosion of the safety basin of this system; the results are verified through numerical simulation. First, the average method is used to approximate the amplitude–frequency relationship of the system, and the accuracy of the analytical results is verified through numerical experiments. Second, the Melnikov method is used to obtain the conditions for the system to enter chaos in the Smale horseshoe sense, and the Melnikov curve is drawn for further verification. Then, bifurcation diagrams are drawn for the changes in various parameters in the system, with a focus on analyzing the influence of friction factors on chaotic bifurcation. By applying the definition and calculation principle of the maximum Lyapunov exponent, and drawing and utilizing the maximum Lyapunov exponent graph, the chaotic state that the system enters under different parameters is more clearly defined. Finally, the evolution law of the safety basin under various parameter changes, especially dry friction changes, is analyzed, and the erosion and bifurcation mechanism of the safety basin is studied. Comparing with the bifurcation diagram, it reveals that chaos primarily contributes to the erosion of the safety basin.

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Dynamic analysis of a class of fractional‐order dry friction oscillators

Si,

Xie,

Zhao

et al. 2024

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

Dynamical behavior of a vertical magnetic pendulum driven by one coil magnet excited by a voltage source

Nyiembui,

Zambo,

Nana

et al. 2024

Nonlinear Dyn

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A novel global perspective: Characterizing the fractal basins of attraction and the level of chaos in a double pendulum

Qin,

Zhang

2024

Chaos, Solitons & Fractals

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Comprehensive analysis of the mechanism of sensitivity to initial conditions and fractal basins of attraction in a novel variable-distance magnetic pendulum

Cited by 4 publications

References 44 publications

Dynamic analysis of a class of fractional‐order dry friction oscillators

Dynamic analysis of a class of fractional‐order dry friction oscillators

Dynamical behavior of a vertical magnetic pendulum driven by one coil magnet excited by a voltage source

A novel global perspective: Characterizing the fractal basins of attraction and the level of chaos in a double pendulum

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