Abstract
The main purpose of this paper is to study the number of limit cycles of sextic polynomial differential systems (SPDS) via the averaging theory which is an extension to the study of cubic polynomial vector fields in (Nonlinear Analysis 66 (2007), 1707--1721), where we provide an accurate upper bound of the maximum number of limit cycles that SPDS can have bifurcating from the period annulus surrounding the origin of a class of cubic system.
Highlights
The main purpose of this paper is to study the number of limit cycles of sextic polynomial differential systems (SPDS) via the averaging theory which is an extension to the study of cubic polynomial vector fields in (Nonlinear Analysis 66 (2007), 1707–1721), where we provide an accurate upper bound of the maximum number of limit cycles that SPDS can have bifurcating from the period annulus surrounding the origin of a class of cubic system
Where f (x, y) = 0 is a conic and f (0, 0) = 0 by using the arbitrary cubic polynomial differential systems provide at least 6 limit cycles bifurcating from the periodic orbits of the period annulus, in [10] the authors found a bound for the number of limit cycles which bifurcate from the period annulus of the center, under piecewise smooth cubic polynomial perturbations
Their results explained that the piecewise smooth cubic system can have at least one more limit cycle than the smooth one, in [1] the author improved the result of the maximum number of limit cycles of quartic and quintic polynomial differential systems which bifurcate from the period annulus surrounding the origin of system (1.1) by using the first order of averaging theory method
Summary
Abstract: The main purpose of this paper is to study the number of limit cycles of sextic polynomial differential systems (SPDS) via the averaging theory which is an extension to the study of cubic polynomial vector fields in (Nonlinear Analysis 66 (2007), 1707–1721), where we provide an accurate upper bound of the maximum number of limit cycles that SPDS can have bifurcating from the period annulus surrounding the origin of a class of cubic system. Their results explained that the piecewise smooth cubic system can have at least one more limit cycle than the smooth one, in [1] the author improved the result of the maximum number of limit cycles of quartic and quintic polynomial differential systems which bifurcate from the period annulus surrounding the origin of system (1.1) by using the first order of averaging theory method.
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