Pitchfork bifurcation and vibrational resonance in a fractional-order Duffing oscillator

Pramana

W Xiang³  H Zhu²  M A F Sanjuán¹  J H Yang1² 

[1] Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain$$;School of Mechanical and Electrical Engineering, China University of Mining and Technology, Xuzhou 221116, People’s Republic of China$$;Department of Mathematics and Computer Science, Huainan Normal University, Huainan 232038, People’s Republic of China$$

关键词: Supercritical pitchfork bifurcation;    subcritical pitchfork bifurcation;    vibrational resonance;    time delay feedback.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

The pitchfork bifurcation and vibrational resonance are studied in a fractional-order Duffing oscillator with delayed feedback and excited by two harmonic signals. Using an approximation method, the bifurcation behaviours and resonance patterns are predicted. Supercritical and subcritical pitchfork bifurcations can be induced by the fractional-order damping, the exciting highfrequency signal and the delayed time. The fractional-order damping mainly determines the pattern of the vibrational resonance. There is a bifurcation point of the fractional order which, in the case of double-well potential, transforms vibrational resonance pattern from a single resonance to a double resonance, while in the case of single-well potential, transforms vibrational resonance from no resonance to a single resonance. The delayed time influences the location of the vibrational resonance and the bifurcation point of the fractional order. Pitchfork bifurcation is the necessary condition for the double resonance. The theoretical predictions are in good agreement with the numerical simulations.

【 授权许可】

Unknown