On bifurcations of a system of cubic differential equations with an integrating multiplier singular along a second-order curve

Abstract

We establish necessary and sufficient conditions for existence of an integrating multiplier of a special form for systems of two cubic differential equations of the first order. We further study bifurcations of such systems with the change of parameters of their integrating multipliers.

Keywords

• integrating multiplier
• cubic differential equations
• bifurcations
• limit cycles