Citation: | GUO Yong, XIE Jian-hua. N-S Bifurcation of an Oscillator With Dry Friction in 1∶4 Strong Resonance[J]. Applied Mathematics and Mechanics, 2013, 34(1): 18-26. doi: 10.3879/j.issn.1000-0887.2013.01.003 |
[1] |
Chatterjee S, Mallik A K.Bifurcations and chaos in autonomous selfexcited oscillators with impact damping[J].Journal of Sound and Vibration,1996,191(4): 539-562.
|
[2] |
Budd C,Dux F,Cliffe A.The effect of frequency and clearance variations on single-degree-of-freedom impact oscillators[J].Journal of Sound and Vibration,1995,184(3):475-502.
|
[3] |
Luo G W, Xie J H. Hopf bifurcations and chaos of a two-degree of-freedom vibro-impact system in two strong resonance cases[J].International Journal of Non-Linear Mechanics,2002,37(1): 19-34.
|
[4] |
谢建华.一类碰撞振动系统的余维二分叉和Hopf分叉[J].应用数学和力学,1996, 17(1):63-73.(XIE Jian-hua. Codimension two bifurcations and Hopf bifurcations of an impacting vibrating system[J]. Appled Mathematics and Mechanics(English Edition),1996,17(1): 65-75.)
|
[5] |
Wen G L.Codimension-2 Hopf bifurcation of a two-degree-of-freedom vibro-impact system[J].Journal of Sound and Vibration,2001,242(3):475-485.
|
[6] |
XIE Jian-hua,DING Wang-cai. Hopf-Hopf bifurcation and invariant torus -T2of a vibro-impact systems[J].International Journal of Non-Linear Mechanics,2005,40(4): 531-543.
|
[7] |
XIE Jian-hua,DING Wang-cai, Dowell E H, Virgin L N. Hopf-flip bifurcation of high dimensional maps and application to vibro-impact systems[J]. Acta Mech Sinica,2005, 21(4):402-410.
|
[8] |
Iooss G.Bifurcation of Maps and Applications[M]. Amsterdam,New York,Oxford: NorthHolland Publishing Company,1979.
|
[9] |
Wan Y H. Bifurcation into invariant tori at points of resonance[J].Archive for Rational Mechanics Analysis,1978,68(4): 343-357.
|