AN ALGORITHM FOR HIGHER-ORDER HOPF NORMAL FORMS

Authors
Citation
Ayt. Leung et T. Ge, AN ALGORITHM FOR HIGHER-ORDER HOPF NORMAL FORMS, Shock and vibration, 2(4), 1995, pp. 307-319
Citations number
NO
Categorie Soggetti
Mechanics
Journal title
ISSN journal
10709622
Volume
2
Issue
4
Year of publication
1995
Pages
307 - 319
Database
ISI
SICI code
1070-9622(1995)2:4<307:AAFHHN>2.0.ZU;2-F
Abstract
Normal form theory is important for studying the qualitative behavior of nonlinear oscillators. In some cases, higher order normal forms are required to understand the dynamic behavior near an equilibrium or a periodic orbit. However, the computation of high-order normal forms is usually quite complicated. This article provides an explicit formula for the normalization of nonlinear differential equations. The higher order normal form is given explicitly. Illustrative examples include a cubic system, a quadratic system and a Duffing-Van der Pol system. We use exact arithmetic and find that the undamped Duffing equation can be represented by an exact polynomial differential amplitude equation in a finite number of terms. (C) 1995 John Wiley & Sons, Inc.