An algorithm for higher order Hopf normal form
Author(s)
Author(s)
Ge, T.
Date Issued
1995
Publisher
Hindawi Publishing Corporation
Journal
Shock and Vibration
Volume
2
Issue
4
Start page
307
End page
319
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.
SFU Affiliated Publication
No
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