On the limit cycles of a class of discontinuous piecewise linear differential systems
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Llibre, Jaume; de A. S. Menezes, Lucyjane;
On the limit cycles of a class of discontinuous piecewise linear differential systems
In this paper we consider discontinuous piecewise linear differential systems whose discontinuity set is a straight line L which does not pass through the origin. These systems are formed by two linear differential systems of the form ̇x= Ax ± b. We study the limit cycles of this class of discontinuous piecewise linear differential systems. We do this study by analyzing the fixed points of the return map of the system defined on the straight line L. This kind of differential systems appear in control theory.
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Limit cycles, return map, limit cycles, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, discontinuous systems, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Discontinuous systems, Discontinuous ordinary differential equations, Return map, Poincaré map
Limit cycles, return map, limit cycles, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, discontinuous systems, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Discontinuous systems, Discontinuous ordinary differential equations, Return map, Poincaré map
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