Abstract
The dynamics as well as the mechanism of various types of multi-mode oscillations in slow-fast coupling system with different ratios between exciting frequencies is investigated. By introducing two periodically changed current sources, a fifth-order generalized BVP coupling circuit is established. For appropriate parameters selected such that the two exciting frequencies are much less than the natural frequency of the system, fast-slow dynamic behaviors under different ratios between two exciting frequencies are investigated. By employing a slow variable so that the two exciting term can be expressed in terms of the slow variable, the original system is divided into fast-slow subsystems. The equilibrium points as well as the related bifurcation conditions are explored, which is employed to investigate the structures of multi-mode oscillation attractors under different ratios between two exciting frequencies. It is found that the system may exhibit multi-mode oscillations with central symmetry, axial symmetry and asymmetry. Different multi-mode oscillations for six cases with different ratios between the exciting frequencies are presented, the mechanism of which is obtained via the fast-slow analysis method upon the transformed phase portraits.
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