NORMAL FORMS OF PLANAR SWITCHING SYSTEMS

作者：Chen, Xingwu; Zhang, Weinian^*

来源：Discrete and Continuous Dynamical Systems, 2016, 36(12): 6715-6736.

DOI：10.3934/dcds.201692

• Switching system
• normal form
• monodromy
• Hopf bifurcation

In this paper we study normal forms of planar differential systems with a non-degenerate equilibrium on a single switching line, i.e., the equilibrium is a non-degenerate equilibrium of both the upper system and the lower one. In the sense of C-0 conjugation we find all normal forms for linear switching systems and use them together with switching near-identity transformations to normalize second order terms, showing the reduction of normal forms. We prove that only one of those 19 types of linear normal form decides if the system is monodromic. With the monodromic linear normal form, we compute the second order monodromic normal form, which gives a condition under which exactly one limit cycle arises from a Hopf bifurcation.

• 出版日期2016-12
• 单位四川大学