Investigation of center manifolds of three-dimensional systems using computer algebra

Authors:
V. G. Romanovski;M. Mencinger;B. Ferčec
Affiliations:
Department of Mathematics, Shanghai Normal University, Shanghai, P. R. China 200234 and Center for Applied Mathematics and Theoretical Physics, University of Maribor, Maribor, Slovenia SI-2000;Faculty of Civil Engineering, University of Maribor, Maribor, Slovenia SI-2000 and Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia SI-1000;Center for Applied Mathematics and Theoretical Physics, University of Maribor, Maribor, Slovenia SI-2000
Venue:
Programming and Computing Software
Year:
2013

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Abstract

For a family of three dimensional systems with center manifolds filled with closed trajectories (corresponding to periodic solutions of the system) we give criteria on the coefficients of the system to distinguish between the cases of isochronous and non-isochronous oscillations. Bifurcations of critical periods of the system are studied as well. The study is performed using computer algebra systems MATHEMATICA and SINGULAR.