Centers and limit cycles of a generalized cubic Riccati system

TL;DR

This paper establishes conditions for centers in a cubic Riccati system and explores bifurcations of small limit cycles from the center components, advancing understanding of nonlinear dynamical behaviors.

Contribution

It provides new criteria for the existence of centers and analyzes bifurcations of small limit cycles in a generalized cubic Riccati system.

Findings

Conditions for the existence of a center are derived.

Bifurcation analysis of small limit cycles is performed.

Insights into the structure of the center variety are provided.

Abstract

We obtain condition for existence of a center for a cubic planar differential system, which can be considered as a polynomial subfamily of the generalized Riccati system. We also investigate bifurcations of small limit cycles from the components of the center variety of the system.