Nonlinear Phenomena in Complex Systems, 2008, Vol.11, No.2, pp.149-157

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2008, Vol.11, No.2, pp.149-157

The Poincaré Map and the Method of Averaging: A Comparative Study.
J. D. Hadjidemetriou

Tow basic methods in the study of nonlinear systems, the Poincaré map and the method of averaging are compared and the advantages and disadvantages of each method are discussed. It is shown that in the regions of the phase space where the system behaves as integrable (smooth invariant curves), the averaged model may give important information on the dynamics. However, in regions where chaotic motion appears, the method of averaging is not applicable. An example is given, illustrating these similarities and differences.
Key words: chaotic motion, Poincaré map

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