Limit cycle bifurcations by perturbing a quadratic integrable system with a triangle

作者：Xiong, Yanqin; Han, Maoan^*; Xiao, Dongmei

来源：Journal of Differential Equations, 2016, 260(5): 4473-4498.

DOI：10.1016/j.jde.2015.11.017

• Quadratic polynomial system
• Homoclinic loop
• Heteroclinic loop
• Triangle
• Limit cycle

Finding cyclicity of homoclinic or heteroclinic loops in quadratic systems is an open problem, which is related to the second part of Hilbert's 16th problem. This paper mainly considers the problem of limit cycle bifurcation for quadratic polynomial systems near a triangle. It is proved that the cyclicity of the triangle in quadratic systems is at least three.

• 出版日期2016-3-5
• 单位上海师范大学; 上海交通大学