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

• Published in: Mathematics and computers in simulation Vol. 221; pp. 281 - 297
• Main Authors: Zhang, Yufeng, Li, Jing, Zhu, Shaotao, Ma, Zerui
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.07.2024
• Subjects: Distributed time delay; Forked bifurcation; Fractional Rayleigh oscillator; Harmonic resonance; Multiple scales method; Harmonic resonance; Fractional Rayleigh oscillator; Forked bifurcation; Distributed time delay; Multiple scales method
• ISSN: 0378-4754; 1872-7166
• DOI: 10.1016/j.matcom.2024.03.008

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.