Bifurcation of limit cycles from an -dimensional linear center inside a class of piecewise linear differential systems
Copyright policy )Bifurcation of limit cycles from an -dimensional linear center inside a class of piecewise linear differential systems
Agraïments: The two first authors are partially supported by a FAPESP-BRAZIL grant 2007/07957-8 and grant 2007/08707-5 respec- tively. Let n be an even integer. We study the bifurcation of limit cycles from the periodic orbits of the n-dimensional linear center given by the differential system x˙ 1 = −x2, x˙ 2 = x1, . . . , x˙ n−1 = −xn, x˙ n = xn−1, perturbed inside a class of piecewise linear differential systems. Our main result shows that at most (4n − 6)n/2−1 limit cycles can bifurcate up to first-order expansion of the displacement function with respect to a small parameter. For proving this result we use the averaging theory in a form where the differentiability of the system is not needed.
Control systems, limit cycles, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, averaging method, Nonlinear ordinary differential equations and systems, Averaging method, Limit cycles, Center, 515, center, piecewise linear differential systems, bifurcation, Piecewise linear differential systems, Bifurcation, Symmetries, invariants of ordinary differential equations, control systems
Control systems, limit cycles, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, averaging method, Nonlinear ordinary differential equations and systems, Averaging method, Limit cycles, Center, 515, center, piecewise linear differential systems, bifurcation, Piecewise linear differential systems, Bifurcation, Symmetries, invariants of ordinary differential equations, control systems
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).7 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!