期刊
JOURNAL OF SOUND AND VIBRATION
卷 326, 期 3-5, 页码 768-779出版社
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jsv.2009.05.012
关键词
-
资金
- Ministry of Science, Republic of Serbia [144008]
In this paper a qualitative analysis of the dynamic systems described with the second-order differential equation with fractional order deflection function is considered. The existence of fixed points, closed orbits and the unions of fixed points and the trajectories connecting them is shown. The homoclinic orbit which connects a fixed point with itself and the corresponding stable and unstable manifolds are given in the closed analytical form. Melnikov's procedure for defining the criteria for transversal intersection of the stable and unstable manifolds is extended for the systems with fractional order deflection function. The critical parameter values for chaos are obtained analytically and proved numerically using the Lyapunov exponents. The bifurcation diagrams are plotted for various values of fractional order and the transition to chaos by period doubling is shown. The phase plane diagrams and the Poincare maps for certain fractional orders are obtained. The control of chaos and the transformation to periodic motion is considered. (C) 2009 Elsevier Ltd. All rights reserved.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据