  In this paper we investigate the isochronicity and linearizability problem
for a cubic polynomial differential system which can be considered as a
generalization of the Riccati system. Conditions for isochronicity and
linearizability are found. The global structure of systems of the family with
an isochronous center is determined. Furthermore, we find the order of weak
center and study the problem of local bifurcation of critical periods in a
neighborhood of the center.
