naa a22 4500 51076763X CHVBK 20180411083202.0 cr unu---uuuuu 180411e20131201xx s 000 0 eng 10.1007/s12043-013-0621-5 doi (NATIONALLICENCE)springer-10.1007/s12043-013-0621-5 Pitchfork bifurcation and vibrational resonance in a fractional-order Duffing oscillator [Elektronische Daten] [J YANG, M SANJUÁN, W XIANG, H ZHU] 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 high-frequency 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. Indian Academy of Sciences, 2013 Supercritical pitchfork bifurcation nationallicence subcritical pitchfork bifurcation nationallicence vibrational resonance nationallicence time delay feedback nationallicence YANG J. School of Mechanical and Electrical Engineering, China University of Mining and Technology, 221116, Xuzhou, People's Republic of China aut SANJUÁN M. Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933, Móstoles, Madrid, Spain aut XIANG W. Department of Mathematics and Computer Science, Huainan Normal University, 232038, Huainan, People's Republic of China aut ZHU H. School of Mechanical and Electrical Engineering, China University of Mining and Technology, 221116, Xuzhou, People's Republic of China aut Pramana Springer India 81/6(2013-12-01), 943-957 0304-4289 81:6<943 2013 81 12043 https://doi.org/10.1007/s12043-013-0621-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s12043-013-0621-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- YANG J. School of Mechanical and Electrical Engineering, China University of Mining and Technology, 221116, Xuzhou, People's Republic of China aut NATIONALLICENCE 700 1- SANJUÁN M. Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933, Móstoles, Madrid, Spain aut NATIONALLICENCE 700 1- XIANG W. Department of Mathematics and Computer Science, Huainan Normal University, 232038, Huainan, People's Republic of China aut NATIONALLICENCE 700 1- ZHU H. School of Mechanical and Electrical Engineering, China University of Mining and Technology, 221116, Xuzhou, People's Republic of China aut NATIONALLICENCE 773 0- Pramana Springer India 81/6(2013-12-01), 943-957 0304-4289 81:6<943 2013 81 12043 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer