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Bifurcation of limit cycles from a two-dimensional center inside. (English) Zbl 1189.34073
Authors’ abstract: We study the bifurcation of limit cycles from the periodic orbits of a linear differential system in n perturbed inside a class of piecewise linear differential systems, which appears in a natural way in control theory. Our main result shows that at most one limit cycle can bifurcate up to first-order expansion of the displacement function with respect to the small parameter. This upper bound is reached. For proving this result we use the averaging theory in a form where the differentiability of the system is not needed.
MSC:
34C23Bifurcation (ODE)
34C05Location of integral curves, singular points, limit cycles (ODE)
34C14Symmetries, invariants (ODE)
34C29Averaging method