Fast-slow analysis for parametrically and externally excited systems with two slow rationally related excitation frequencies.
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.
Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang Jiangsu 212013, People's Republic of China.
Xiujing
X
Han
Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang Jiangsu 212013, People's Republic of China.
Qinsheng
Q
Bi
Potsdam Institute for Climate Impact Research, Potsdam 14473, Germany.|Department of Physics, Humboldt University, Berlin 12489, Germany.
Peng
P
Ji
Potsdam Institute for Climate Impact Research, Potsdam 14473, Germany.|Department of Physics, Humboldt University, Berlin 12489, Germany.|Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom.|Department of Control Theory, Nizhny Novgorod State University, Gagarin Avenue 23, 606950 Nizhny Novgorod, Russia.
Jürgen
J
Kurths
D008962:Models, Theoretical; D010507:Periodicity