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Bifurcation of limit cycles from a four-dimensional center in control systems. (English) Zbl 1092.34519
Summary: We study the bifurcation of limit cycles from the periodic orbits of a four-dimensional center in a class of piecewise linear differential systems, which appears in a natural way in control theory. Our main result shows that three is an upper bound for the number of limit cycles, up to first-order expansion of the displacement function with respect to the small parameter. Moreover, this upper bound is reached. For proving this result, we use the averaging method in a form where the differentiability of the system is not needed.

34C05Location of integral curves, singular points, limit cycles (ODE)
37G15Bifurcations of limit cycles and periodic orbits
37N35Dynamical systems in control
93C15Control systems governed by ODE
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