一类平面分段光滑线性系统极限环个数的估计

Estimation of number of limit cycles for a class of planar piecewise smooth linear system

利用Hamilton函数改变量,研究一类平面分段光滑线性系统,给出了其一阶Melnikov函数的计算公式,并证明了该系统可以存在5个极限环.

By using Hamiltonian function variation, a class of planar piecewise smooth linear system is studied. The calcula-tion formula of first-order Melnikov function is given and the conclusion that the planar piecewise smooth linear system canexist 5 limit cycles is proved.