Harmonic resonance and bifurcation of fractional Rayleigh oscillator with distributed time delay

Yufeng Zhang, Jing Li, Shaotao Zhu and Zerui Ma

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 221, issue C, 281-297

Abstract: Resonance and bifurcation are prominent and significant features observed in various nonlinear systems, often leading to catastrophic failure in practical engineering. This paper investigates, under an analytical and numerical perspective, the dynamical characteristics of a fractional Rayleigh oscillator with distributed time delay. Firstly, through the application of the multiple scales method, we derive approximated analytical solutions and amplitude–frequency equations for the regions near both primary and secondary resonances. The stability conditions of steady-state motions and the existence region of the subharmonic response are also obtained. Furthermore, to validate the accuracy of the approximated solutions, the results are compared with numerical solutions derived from the Caputo scheme, revealing a high concordance between them. Then, a comprehensive study on response curves is conducted for the system under different nonlinear damping, fractional parameters and delay strength. Finally, we identify and discuss the presence of the forked bifurcation within the system.

Keywords: Fractional Rayleigh oscillator; Harmonic resonance; Forked bifurcation; Distributed time delay; Multiple scales method (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:221:y:2024:i:c:p:281-297

DOI: 10.1016/j.matcom.2024.03.008

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