Noise activated transitions among periodic states of a pendulum with a vertically oscillating pivot, mediated by a chaotic attractor

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 462, Issue 2067, 2006, Pages 1043-1052

  Blackburn, James A ^a  

^a WILFRID LAURIER UNIVERSITY   (Canada)

Author keywords

Chaos; Dynamic wells; Inverted pendulum; Noise activation

Indexed keywords

EID: 33845538310     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2005.1630     Document Type: Article

References (15)

1. Acheson, D. J. 1995 Multiple-nodding oscillations of a driven inverted pendulum. Proc. R. Soc. A 448, 89-95.
2. Baker, G. L. & Blackburn, J. A. 2005 The pendulum: a case study in physics, pp. 263-266. Oxford: Oxford University Press.
3. Bartuccelli, M. V., Gentile, G. & Georgiou, K. V. 2001 On the dynamics of a vertically driven damped planar pendulum. Proc. R. Soc. A 457, 3007-3022. (doi:10.1098/rspa.2001.0841)
4. Blackburn, J. A., Smith, H. J. T. & Grønbech-Jensen, N. 1992 Stability and Hopf bifurcations in an inverted pendulum. Am. J. Phys. 60, 903-908. (doi:10.1119/1.17011)
5. Blackburn, J. A., Gronbech-Jensen, N. & Smith, H. J. T. 1995 Stochastic noise and chaotic transients. Phys. Rev. Lett. 74, 908-911. (doi:10.1103/PhysRevLett.74.908)
6. Butikov, E. I. 2001 On the dynamic stabilization of an inverted pendulum. Am. J. Phys. 69, 755-768. (doi:10.1119/1.1365403)
7. Clifford, M. J. & Bishop, S. R. 1998 Inverted oscillations of a driven pendulum. Proc. R. Soc. A 454, 2811-2817. (doi:10.1098/rspa.1998.0282)
8. Hilborn, R. C. 1994 Chaos and nonlinear dynamics, pp. 304-313. New York: Oxford University Press.
9. Kim, S.-Y. & Hu, B. 1998 Bifurcations and transitions to chaos in an inverted pendulum. Phys. Rev. E 58, 3028-3035. (doi:10.1103/PhysRevE.58.3028)
10. Kramers, H. A. 1940 Brownian motion in a field of force and the diffusion model of chemical reactions. Physica VII, 284-304. (doi:10.1016/S0031-8914(40) 90098-2)
11. Landau, L. D. & Lifshitz, E. M. 1976 Mechanics. 3rd edn., pp. 93-95. New York: Pergamon Press.
12. Leiber, T. & Risken, H. 1988 Stability of parametrically excited dissipative systems. Phys. Lett. A 129, 214-218. (doi:10.1016/0375-9601(88) 90352-0)
13. Leven, R. W. & Koch, B. P. 1981 Chaotic behaviour of a parametrically excited damped pendulum. Phys. Lett. 86A, 71-74.
14. Smith, H. J. T. & Blackburn, J. A. 1994 Multiperiodic orbits in a pendulum with a vertically oscillating pivot. Phys. Rev. E 50, 539-545. (doi:10.1103/PhysRevE.50.539)
15. Stephenson, A. 1908 On a new type of dynamic stability. Mem. Proc. Manch. Lit. Phil. Soc. 52, 1-10.