Self-reanimating chaos in the bouncing-ball system
作者： Zbigniew J. Kowalik , Marek Franaszek , Piotr Pierański
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摘要: The bouncing-ball problem was studied both experimentally and numerically. A qualitatively new behavior---so-called ``self-reanimating'' chaos---was found. In the experiment this behavior can be regarded as fully chaotic, but treated regular motion (a cycle of large period) in analytical approach.
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sci-hub.se 参考文章(15)
A. J. Lichtenberg, M. A. Lieberman, Regular and Stochastic Motion Applied Mathematical Sciences. ,(1983) , 10.1007/978-1-4757-4257-2
A.J. Lichtenberg, M.A. Lieberman, R.H. Cohen, Fermi acceleration revisited Physica D: Nonlinear Phenomena. ,vol. 1, pp. 291- 305 ,(1980) , 10.1016/0167-2789(80)90027-5
P.J. Holmes, The dynamics of repeated impacts with a sinusoidally vibrating table Journal of Sound and Vibration. ,vol. 84, pp. 173- 189 ,(1982) , 10.1016/S0022-460X(82)80002-3
Boris V Chirikov, A universal instability of many-dimensional oscillator systems Physics Reports. ,vol. 52, pp. 263- 379 ,(1979) , 10.1016/0370-1573(79)90023-1
P. Pierański, Jumping particle model. Period doubling cascade in an experimental system Journal De Physique. ,vol. 44, pp. 573- 578 ,(1983) , 10.1051/JPHYS:01983004405057300
Pi. Pierański, Z. Kowalik, M. Franaszek, Jumping particle model. A study of the phase space of a non-linear dynamical system below its transition to chaos Journal de Physique. ,vol. 46, pp. 681- 686 ,(1985) , 10.1051/JPHYS:01985004605068100
N.B. Tufillaro, T.M. Mello, Y.M. Choi, A.M. Albano, Period doubling boundaries of a bouncing ball Journal De Physique. ,vol. 47, pp. 1477- 1482 ,(1986) , 10.1051/JPHYS:019860047090147700
T. M. Mello, N. B. Tufillaro, Strange attractors of a bouncing ball American Journal of Physics. ,vol. 55, pp. 316- 320 ,(1987) , 10.1119/1.15194
Celso Grebogi, Edward Ott, James A. Yorke, Crises, sudden changes in chaotic attractors, and transient chaos Physica D: Nonlinear Phenomena. ,vol. 7, pp. 181- 200 ,(1983) , 10.1016/0167-2789(83)90126-4
H. Kantz, P. Grassberger, Repellers, semi-attractors, and long-lived chaotic transients Physica D: Nonlinear Phenomena. ,vol. 17, pp. 75- 86 ,(1985) , 10.1016/0167-2789(85)90135-6