Periodic solutions of a quartic nonautonomous equation
Non-Linear Analysis
Computing centre conditions for certain cubic systems
Journal of Computational and Applied Mathematics
Hi-index | 7.29 |
We investigate the planar analytic systems which have a center-focus equilibrium at the origin and whose angular speed is constant. The conditions for the origin to be a center (in fact, an isochronous center) are obtained. Concretely, we find conditions for the existence of a Cw-commutator of the field. We cite several subfamilies of centers and obtain the centers of the cuartic polynomial systems and of the families (-y + x(H1 + Hm), x + y(H1 + Hm)t and (-y + x(H2 + H2n), x + y(H2 + H2n))t, with Hi homogeneous polynomial in x,y of degree i. In these cases, the maximum number of limit cycles which can bifurcate from a fine focus is determined.