This paper investigates the Hopf cyclicity of a piecewise smooth quadratic polynomial system by Melnikov function method, whose unperturbed system is a concrete reversible quadratic system with a center at the origin and with a non-rational first integral. By comparing the obtained result for the piecewise case with the result for the smooth case, it shows that the piecewise system can have at least four more limit cycles around the origin than the smooth one.

中文翻译：

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具有非理性第一积分的可逆二次系统摄动的极限环分支

本文利用Melnikov函数方法研究了分段光滑二次多项式系统的Hopf循环，该系统的无扰动系统是一个以原点为中心，第一阶非有理积分的可逆二次系统。通过将分段情况下的结果与平滑情况下的结果进行比较，可以看出，分段系统在原点周围的极限循环至少可以比平滑系统多四个极限循环。