# Linearizability and critical period bifurcations of a generalized Riccati system

## TL;DR

This paper studies when a generalized Riccati system exhibits isochronicity and linearizability, identifying conditions, global structures, and bifurcation behaviors of critical periods near centers.

## Contribution

It provides new conditions for isochronicity and linearizability in a generalized Riccati system, and analyzes bifurcations of critical periods.

## Key findings

- Conditions for isochronicity and linearizability are established.
- Global structure of systems with an isochronous center is characterized.
- Order of weak centers and bifurcation of critical periods are analyzed.

## Abstract

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.