This paper is devoted to the study of limit cycles that can bifurcate of a perturbation of piecewise non-Hamiltonian systems with nonlinear switching manifold. We derive the first order Melnikov function to these systems. As application, the sharp upper bound of the number of bifurcated limit cycles of two concrete systems, whose switching manifolds are algebraic curves, is presented.

中文翻译：

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带有非线性切换流形的分段非哈密顿系统的极限环分岔

本文致力于极限环的研究，该极限环可以使带有非线性切换流形的分段非哈密顿系统的扰动分叉。我们将一阶Melnikov函数推导到这些系统。作为应用，给出了两个混凝土系统的分叉极限环数量的尖锐上限，其切换歧管为代数曲线。