On the Number of Limit Cycles by Perturbing a Piecewise Smooth Liénard Model

In this paper, we study the number of limit cycles by perturbing a Lienard model ẋ = y, ẏ = −g(x), where g(x) is piecewise smooth. Under the assumption that the unperturbed Lienard type system has a family of periodic orbits, we first deduce the expression for its first order Melnikov function, and then obtain the maximum number of limit cycles bifurcating from the period annulus.

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