Limit cycles of continuous piecewise differential systems separated by a parabola and formed by a linear center and a quadratic center
Copyright policy )Limit cycles of continuous piecewise differential systems separated by a parabola and formed by a linear center and a quadratic center
Due to their applications to many physical phenomena during these last decades the interest for studying the continuous or discontinuous piecewise differential systems has increased strongly. The limit cycles play a main role in the study of any planar differential system. Up to now the major part of papers which study the limit cycles of the planar piecewise differential systems have considered systems formed by two pieces separated by one straight line. Here we consider planar continuous piecewise differential systems separated by a parabola. We prove that the planar continuous piecewise differential systems separated by a parabola and formed by a linear center and a quadratic center have at most one limit cycle. Moreover there are systems in this class exhibiting one limit cycle. So in particular we have solved the extension of the 16th Hilbert problem to this class of differential systems.
Quadratic center, quadratic center, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, Continuous piecewise differential system, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, linear center, continuous piecewise differential system, Limit cycle, Linear center, limit cycle, Bifurcations of limit cycles and periodic orbits in dynamical systems
Quadratic center, quadratic center, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, Continuous piecewise differential system, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, linear center, continuous piecewise differential system, Limit cycle, Linear center, limit cycle, Bifurcations of limit cycles and periodic orbits in dynamical systems
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