Limit cycles in planar piecewise linear differential systems with nonregular separation line
Copyright policy )Limit cycles in planar piecewise linear differential systems with nonregular separation line
Agraïments: The first author is supported by FAPESP grant number 2013/24541-0 and CAPES grant number 88881.030454/2013-01 Program CSF-PVE and UNAB13-4E-1604. In this paper we deal with lanar piecewise linear differential systems defined in two zones. We consider the case when the two linear zones are angular sectors of angles and 2 - respectively, for (0,). We study the problem of determining lower bounds for the number of isolated periodic orbits in such systems using Melnikov functions. These limit cycles appear studying higher order piecewise linear perturbations of a linear center. It is proved that the maximum number of limit cycles that can appear up to a sixth order perturbation is five. Moreover, for these values of we prove the existence of systems with four limit cycles up to fifth order and, for =/2, we provide an explicit example with five up to sixth order. In general, the nonregular separation line increases the number of periodic orbits in comparison with the case where the two zones are separated by a straight line.
Perturbations, asymptotics of solutions to ordinary differential equations, two zones, Nonregular separation line, 515, Limit cycle in Melnikov higher order perturbation, nonregular separation line, Non-smooth differential systems in two zones, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, limit cycle in Melnikov higher order perturbation, nonsmooth differential systems, Discontinuous ordinary differential equations, Periodic solutions to ordinary differential equations
Perturbations, asymptotics of solutions to ordinary differential equations, two zones, Nonregular separation line, 515, Limit cycle in Melnikov higher order perturbation, nonregular separation line, Non-smooth differential systems in two zones, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, limit cycle in Melnikov higher order perturbation, nonsmooth differential systems, Discontinuous ordinary differential equations, Periodic solutions to ordinary differential equations
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).57 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.Top 1% 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!