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In this paper, we generalize the Picard-Fuchs equation method to study thebifurcation of limit cycles of perturbed differential systems with twoswitching lines. We obtain the detailed expression of the corresponding firstorder Melnikov function which can be used to get the upper bound of the numberof limit cycles for the perturbed system by using Picard-Fuchs equation. It isworth noting that we greatly simplify the computations and this method can beapplied to study the number of limit cycles of other differential systems withtwo switching lines. Our results also show that the number of switching lineshas essentially impact on the number of limit cycles bifurcating from a periodannulus.

Bifurcation of limit cycles from a quadratic global center with two switching lines