Computation of Floquet Multipliers Using an Iterative Method for Variational Equations

Yu NUREKI  Sunao MURASHIGE  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E92-A   No.5   pp.1331-1338
Publication Date: 2009/05/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E92.A.1331
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Numerical Analysis and Optimization
Keyword: 
numerical method,  stability,  ordinary differential equations,  periodic orbits,  Floquet multipliers,  

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Summary: 
This paper proposes a new method to numerically obtain Floquet multipliers which characterize stability of periodic orbits of ordinary differential equations. For sufficiently smooth periodic orbits, we can compute Floquet multipliers using some standard numerical methods with enough accuracy. However, it has been reported that these methods may produce incorrect results under some conditions. In this work, we propose a new iterative method to compute Floquet multipliers using eigenvectors of matrix solutions of the variational equations. Numerical examples show effectiveness of the proposed method.