一类具有线性尖点的1:2共振向量场的极限环

Limit cycles of a class of planar system with 1 : 2 resonance for linear cusp

作者讨论了具有线性尖点的1:2共振平面向量场=y,=x(1-x^2)(3-x^2)+μ(ξ_0+ξ_1x^2-x^4)y 的非局部分岔,其中 x,y∈R,参数ξ_0,ξ_1∈R且|μ|《1.通过讨论其相应的 Picard-Fuchs 方程,作者给出了由 Poincar分岔和异宿轨分岔出极限环的条件.

The authors discuss the nonlocal bifurcation of a class of planar system with 1：2 resonance for linear cuspx = y ,y = x（1 -x^2）（3-x^2）＋μ（ε0＋ε1x^2-x^4）y , where x,y∈R,parameters ε0,ε1∈R and ｜μ｜〈〈1 . By studying Picard-Fuchs equation,the authors give conditions for limit cycles arising from Poincaré bifurcation and heteroclinic bifurcation.