一类大阻尼非自治摆系统的周期解与混沌态
Periodic Solution and Chaotic Behavior of a Class of Nonautonomic Pendulum Systems with Large Damping
-
摘要: 本文研究二阶非自治摆型系统的周期解的存在性和唯一性,并研究了φ(t)=1-ελcosωt,F(t)=β+εμ(cosωt-ωsinωt)a>0为大阻尼系数时该系统呈现混沌性态的参数区域.所得结果推广了文[1～8]中的相应结论.Abstract: 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 tor which the system in chaos is myestigated when φ(t)=1-ελcosωt,F(t)=β+εμ(cosωt-ωsinωt) and the tamping coefficient a>0 is large. The result obtained generalize the corresponding conclusions of papers [1-8].
-
[1] Sun Jian-hua. Chaotic motions of the pendulum systems, J. Nanjing University, Math. Biquarterly, 4. 1 (1987), 43-50. (in chinese) [2] 钱敏等,Josephson结的I-V曲线的理论分析,物理学报,36. 2 (1987),149-156. [3] 王荣良,调频输入正弦锁相环路的研究,工程数学学报,3. 2 (1986),142-144. [4] Sansone, G. and R. Conti, Nonlinear Differential Equation, Pergamon Press (1964). [5] Bcasley, M.R. and B.A. Huberman, Chaos in Joscphson junctions, Comm. Sol. Sta. Phys., 10 (1982), 155-162. [6] Ben-Jacob, E., et al., Intermittent chaos in Josephson junctions, Phys. Rev. Lutt., 49 (1982), 1599-1602. [7] Cirillo, M. and N.F. Pederson, On bifurcations and transition to chaos in a Josephson junctions, Phys, Lett, 90A (1982). 150-152. [8] Guckcnhcimer J. and P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer-Verlag (1983). [9] Lasalle. J.I. and S, Lefsechetz, Stability by Lyapunov's Direct Method with Application. New York, Academic Press (1961). -
点击查看大图
计量
- 文章访问数: 1593
- HTML全文浏览量: 61
- PDF下载量: 464
- 被引次数: 0
下载:
