Dynamics at Infinity and Existence of Singularly Degenerate Heteroclinic Cycles in Maxwell–Bloch System

Abstract

In this paper, global dynamics of the Maxwell–Bloch system is discussed. First, the complete description of its dynamic behavior on the sphere at infinity is presented by using the Poincaré compactification in R3. Second, the existence of singularly degenerate heteroclinic cycles is investigated. It is proved that for a suitable choice of the parameters, there is an infinite set of singularly degenerate heteroclinic cycles in Maxwell–Bloch system. Specially, the chaotic attractors are found nearby singularly degenerate heteroclinic cycles in Maxwell–Bloch system by combining theoretical and numerical analyses for a special parameter value. It is hoped that these theoretical and numerical value results are given a contribution in an understanding of the physical essence for chaos in the Maxwell–Bloch system.