Poincaré Bifurcation of a Cubic System with Parabolic Arch Boundary and Periodic Ring

Abstract:

      By specific examples, we show that Poincaré' bifurcation of a polynomial system, being of period annulus with the same degree and the same boundary, can produce different number of limit cycles because of different closed orbits in period annulus.Thus,a new approach is created for the study of weakened Hilbert's 16^th problem of polynomial system.