Global dynamics of the Maxwell–Bloch system with invariant algebraic surfaces

Abstract

In this paper by using the Poincaré compactification in we make a global analysis of the Maxwell–Bloch system with , b, c and . We give the complete description of its dynamics on the sphere at infinity. For some values of the parameters, this system has first integrals and invariant algebraic surfaces. For these sets, we provide the global phase portraits of the Maxwell–Bloch system in the Poincaré ball (i.e. in the compactification of with the sphere at infinity).