Periodic solution and chaotic behavior of a class of nonautonomic pendulum systems with large damping
- 20 Downloads
In this paper the existence and uniqueness of the periodic solution is studied for a class of second order nonautonomic pendulum systems
and the parameter regions for which the system in chaos is investigated when
$$\bar x + a\dot x + \varphi (t)\sin x = F(t)$$
and the damping coefficient a>0 is large. The results obtained generalize the corresponding conclusions of papers [1–8].
$$\varphi (t) = 1 - \varepsilon \lambda \cos \omega t, F(t) = \beta + \varepsilon \mu (\cos \omega t - \omega \sin \omega t)$$
KeywordsMathematical Modeling Periodic Solution Industrial Mathematic Chaotic Behavior Parameter Region
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Unable to display preview. Download preview PDF.
- Sun Jian-hua, Chaotic motions of the pendulum systems.J. Nanjing University, Math. Biquarterly,4, 1 (1987), 43–50. (in chinese)Google Scholar
- Qían Min, et al., Theoretic analysis of I–V characteristics in Josephson junction.Acta Physica Sinica,36, 2 (1987), 149–156. (in Chinese)Google Scholar
- Wang Rong-liang, Research of a P-L-L with sine characteristic and frequency modulation.J. Engin. Math.,3, 2 (1986), 142–144. (in Chinese)Google Scholar
- Sansone, G. and R. Conti,Nonlinear Differential Equation. Pergamon Press (1964).Google Scholar
- Beasley, M.R. and B.A. Huberman, Chaos in Josephson junctions.Comm. Sol. Sta. Phys.,10 (1982), 155–162.Google Scholar
- Ben-Jacob, E., et al., Intermittent chaos in Josephson junctions,Phys. Rev. Lett.,49 (1982), 1599–1602.Google Scholar
- Cirillo, M. and N.F. Pederson, On bifurcations and transition to chaos in a Josephson junctions,Phys. Lett. 90A (1982), 150–152.Google Scholar
- Guckenheimer, J. and P. Holmes,Nonlinear Oscillations. Dynamical Systems and Bifurcations of Vector Fields. Springer-Verlag (1983).Google Scholar
- Lasalle, J.I., and S. Lefschetz,Stability by Lyapunov's Direct Method with Application. New York, Academic Press (1961).Google Scholar
© Shanghai University of Technology (SUT) 1988