On the Number of Limit Cycles Bifurcating from the Bogdanov–Takens System with an Algebraic Switching Curve

In this paper, we consider the bifurcation of limit cycles from the Bogdanov–Takens system with an algebraic switching curve under perturbations of piecewise smooth polynomials of degree n. By using Picard–Fuchs equations and the Chebyshev criterion, we give the upper bound of the number of limit cycles that bifurcate from the period annulus for the piecewise smooth Bogdanov–Takens system if the first-order Melnikov function is not identically 0.