Vibration resonance and fork bifurcation of under-damped Duffing system with fractional and linear delay terms

Xie, Jiaquan; Guo, Rong; Ren, Zhongkai; He, Dongping; Xu, Huidong

doi:10.1007/s11071-023-08462-2

Nonlinear Dyn

2023

DOI: 10.1007/s11071-023-08462-2

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Vibration resonance and fork bifurcation of under-damped Duffing system with fractional and linear delay terms

Jiaquan Xie

Rong Guo

Zhongkai Ren

et al.

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Cited by 9 publications

References 43 publications

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Solvability of nonlocal fractional vector functional boundary value problems with p‐Laplacian on a half‐line at resonance

Meng,

Jiang,

Zhou

2024

Math Methods in App Sciences

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In this paper, the solvability of a system of fully nonlinear Hilfer fractional differential equations on the half‐line is studied. Firstly, considering that the half‐line as the domain has the problem of insufficient compactness, we defined the space of weighting functions and normed the convergence at infinity. Secondly, by constructing appropriate operators in these Banach spaces and using the extension for the continuous theorem, some sufficient conditions for the solvability of the problem are obtained. Finally, an example is given to illustrate the main results.

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Solvability of nonlocal fractional vector functional boundary value problems with p‐Laplacian on a half‐line at resonance

Meng,

Jiang,

Zhou

2024

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

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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Control of Hopf bifurcation for a four-dimensional fractional order hyperchaotic system with coexisting attractors

Wang,

Zhang,

Liu

et al. 2024

Nonlinear Dyn

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Vibration resonance and fork bifurcation of under-damped Duffing system with fractional and linear delay terms

Cited by 9 publications

References 43 publications

Solvability of nonlocal fractional vector functional boundary value problems with p‐Laplacian on a half‐line at resonance

Solvability of nonlocal fractional vector functional boundary value problems with p‐Laplacian on a half‐line at resonance

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

Control of Hopf bifurcation for a four-dimensional fractional order hyperchaotic system with coexisting attractors

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