中文摘要：

探讨了慢变外激励下的Van der Pol-Duffing系统的复杂动力学行为,揭示了由于慢变外激励的存在而使系统产生的两时间尺度混合模式振动及其动力学机理.当快子系统的平衡点失稳时,快子系统可以呈现出两种不同的动力学特性,即所谓的“单稳态”和“双稳态”.探讨了与“单稳态”和“双稳态”相关的混合模式振动,得到了三类不同的振动模式,即对称式“delayed sup Hopf/delayed sup Hopf”型,对称式“sub Hopf/fold-cycle”型,以及对称式“sub Hopf/sub Hopf”型.

英文摘要：

This paper investigates the complex dynamical behaviors in the Van der Pol-Dutting system with a slowly varying external forcing. Two-time-scale mixed-mode oscillations （MMOs）, resulted from the presence of slowly changing external forcing, are revealed and discussed. When the fast subsystem loses its equilibrium stability, it shows two different dynamical characteristics, i.e., the so-called ＂mono-stability＂ and ＂bi-stability＂. The MMOs of both the ＂mono-stability＂ and ＂bi-stability＂ characters are studied, and three different kinds of symmetric MMOs are obtained, i.e., the ＂delayed supHopf/delayed supHopf＂ type, the ＂subHopf/fold cycle＂ type and the ＂subHoptTsubHopf＂ type.