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Limit cycle bifurcations from a quadratic center with two switching lines. (English) Zbl 1450.34025

In this paper, the authors deal with limit cycle bifurcations for a differential system with two switching lines by using the Picard-Fuchs equation. The detailed expression of the corresponding first order Melnikov function which can be used to get the upper bound of the number of limit cycles is derived. The obtained results indicate that the number of switching lines plays a key role in describing the number of limit cycles bifurcating from a period annulus.

MSC:

34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34A36 Discontinuous ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations
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