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

Author(s)

Dias, F. S. ^[1] ; Valls, Claudia ^[2]

Affiliation

^[1] Univ Fed Itajuba, Inst Matemat & Comp, Itajuba - Brazil

^[2] Univ Lisbon, Inst Super Tecn, Dept Matemat, Lisbon - Portugal

• Document type: Journal article
• Source: DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL; v. 35, n. 4, p. 668-681, OCT 1 2020.
• Web of Science Citations: 0

Abstract

In this paper by using the Poincare compactification in R-3, we make a global analysis of the Maxwell- Bloch system (x) over dot = y, (y) over dot = cy + dx - xz (z) over dot = bz + xy with (x, y, z) is an element of R-3, b, c and d is an element of R. 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 Poincare ball (i.e. in the compactification of R-3 with the sphere S-2 at infinity). (AU)

• FAPESP's process: 17/20854-5 - Qualitative theory of ordinary differential equations: integrability, periodic orbits and phase portraits
• Grantee: Regilene Delazari dos Santos Oliveira
• Support Opportunities: Regular Research Grants