Nonlinear Phenomena in Complex Systems, 2006, Vol.9, No.2, pp.133-140

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2006, Vol.9, No.2, pp.133-140

Nonlinear Normal Forms for Non-Normal Fixed Points.
Bruno Eckhardt and Daniel P. Lathrop

We consider the effects of non-linearities on the transients growth near stationary points where the matrices of the linearization are not normal and study in particular the influence of non-normality on the basin of attraction of the stationary solution. Specifically, for the case of two degrees of freedom and quadratic and cubic nonlinearities, we identify the dominant non-linearities and how they together with the non-normal growth limit the stability basin.
Key words: non-normal amplification, stability

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