Stability of a 2-dimensional Mathieu-type system with quasiperiodic coefficients

Research output: Contribution to journalArticlepeer-review


In the following we consider a 2-dimensional system of ODEs containing quasiperiodic terms. The system is proposed as an extension of Mathieu-type equations to higher dimensions, with emphasis on how resonance between the internal frequencies leads to a loss of stability. The 2-d system has two ‘natural’ frequencies when the time-dependent terms are switched off, and it is internally driven by quasiperiodic terms in the same frequencies. Stability charts in the parameter space are generated first using numerical simulations and Floquet theory. While some instability regions are easy to anticipate, there are some surprises: within instability zones, small islands of stability develop, and unusual ‘arcs’ of instability arise also. The transition curves are analyzed using the method of harmonic balance, and we find we can use this method to easily predict the ‘resonance curves’ from which bands of instability emanate. In addition, the method of multiple scales is used to examine the islands of stability near the 1:1 resonance.
Original languageEnglish
Pages (from-to)341-356
Number of pages16
JournalNonlinear Dynamics
Issue number3
Publication statusPublished - 2010


Dive into the research topics of 'Stability of a 2-dimensional Mathieu-type system with quasiperiodic coefficients'. Together they form a unique fingerprint.

Cite this