In this paper, we study the local bifurcation of critical periods near the nondegenerate center （the origin） of a class of Li@nard equations with degree 2n, and prove that at most 2n - 2 critical periods （taken into account multiplicity） can be produced from a weak center of finite order. We also prove that it can have exactly 2n - 2 critical periods near the origin.
This paper is concerned with limit cycles which bifurcate from a period annulus of a quadratic reversible Lotka-Volterra system with sextic orbits.The authors apply the property of an extended complete Chebyshev system and prove that the cyclicity of the period annulus under quadratic perturbations is equal to two.
This paper is concerned with the quadratic perturbations of a one-parameter family of quadratic reversible system, having a center of genus one. The exact upper bound of the number of limit cycles emerging from the period annulus surrounding the center of the unperturbed system is given.
