Mixed-Mode Oscillations in Wang Model

【作者】 刘伟明； 谢勇；

【Author】 LIU Wei-ming;XIE Yong;State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University;

【机构】 State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University；

【摘要】 We elaborate the transit among all oscillations that the Wang model can exhibit,and explain a bistable region how to appear and disappear again.Especially,mixed-mode oscillations are important phenomena to which we devote ourselves in this paper.By reducing the four-dimensional Wang model to a two-dimensional model and making use of dynamical properties of critical manifold,we find the mixed-mode oscillations in the Wang model are closely related to canard explosion,and the unstable equilibriums on the repelling slow manifold play a key role in the pattern of mixed-mode oscillations.更多还原

【Abstract】 We elaborate the transit among all oscillations that the Wang model can exhibit, and explain a bistable region how to appear and disappear again. Especially, mixed-mode oscillations are important phenomena to which we devote ourselves in this paper. By reducing the four-dimensional Wang model to a two-dimensional model and making use of dynamical properties of critical manifold, we find the mixed-mode oscillations in the Wang model are closely related to canard explosion, and the unstable equilibriums on the repelling slow manifold play a key role in the pattern of mixed-mode oscillations.更多还原