Abstract
We present a general method for analyzing mixed-mode oscillations (MMOs) in parametrically and externally excited systems with two low excitation frequencies (PEESTLEFs) for the case of arbitrary m:n relation between the slow frequencies of excitations. The validity of the approach has been demonstrated using the equations of Duffing and van der Pol, separately. Our study shows that, by introducing a slow variable and finding the relation between the slow variable and the slow excitations, PEESTLEFs can be transformed into a fast-slow form with a single slow variable and therefore MMOs observed in PEESTLEFs can be understood by the classical machinery of fast subsystem analysis of the transformed fast-slow system.
| Original language | English |
|---|---|
| Article number | 012911 |
| Number of pages | 12 |
| Journal | Physical Review. E, Statistical, Nonlinear and Soft Matter Physics |
| Volume | 92 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 15 Jul 2015 |
Bibliographical note
ACKNOWLEDGMENTSThe authors express their gratitude to the anonymous
reviewers for their valuable comments and suggestions that
help to improve the paper. This work was supported by the
National Natural Science Foundation of China (Grants No.
11202085, No. 21276115, No. 11302087, No. 11302086,
and No. 11402226), the Natural Science Foundation of
Jiangsu Province (Grant No. BK20130479), and the Research
Foundation for Advanced Talents of Jiangsu University (Grant
No. 11JDG075 ).
Keywords
- mixed-mode oscillations
- HOPF-bifurcation
- catalyst deactivation
- passage
- modulation
- dynamics
- patterns
- period
- chaos
- weak