Dynamical system theory has developed rapidly over the past fifty years. It is a subject upon
which the theory of limit cycles has a significant impact for both theoretical advances and …

This paper deals with the period function of the reversible quadratic centers X ν=− y (1− x)∂
x+(x+ D x 2+ F y 2)∂ y, where ν=(D, F)∈ R 2. Compactifying the vector field to S 2, the …

Given a C∞ family of planar vector fields {X μ ˆ} μ ˆ∈ W ˆ having a hyperbolic saddle, we
study the Dulac map D (s; μ ˆ) and the Dulac time T (s; μ ˆ) between two transverse sections …

In this paper, we consider local critical periods of planar vector field. Particular attention is
given to revertible systems with polynomial functions up to third degree. It is assumed that …

In this paper, we consider the weak center conditions and local critical periods for a Z_ 2 Z 2-
equivariant cubic system with eleven center conditions at the bi-center. Using the computer …

This paper considers the critical periods of third-order planar Hamiltonian systems. It is
assumed that the origin of the system is a center. With the aid of symbolic and numerical …

In this paper, we study the relationship between period and energy of periodic traveling
wave solutions for the φ 6 field model. The various topological phase portraits with periodic …

In this paper we consider several families of potential non-isochronous systems and study
their associated period functions. Firstly, we prove some properties of these functions, like …

The present work introduces the problem of simultaneous bifurcation of limit cycles and
critical periods for a system of polynomial differential equations in the plane. The …

In this paper we consider planar potential differential systems and we study the bifurcation of
critical periodic orbits from the outer boundary of the period annulus of a center. In the …