Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Neimark-saker Bifurcation and the Dynamics of Laser with Saturable Absorber

Author(s):

Dmitriy Yurievich Volkov

Dept. of High Geometry
Faculty of Mathematics and Mechanics
Saint-Petersburg State University

dmitrivolkov@mail.ru

Ksenia Valerievna Galunova

Dept. of High Mathematics
Peter the Great St.Petersburg Polytechnic University

Abstract:

In this paper we investigate the dynamics associated with multiple bifurcation that arises in laser with saturable absorber (LSA). We study bifurcation of periodic solutions and invariant tori from an equilibrium point of LSA equations for which the linearisation has a pair of pure imaginary eigenvalues and a double zero eigenvalue of index two. The approach is based on the central manifold reduction and the method of normal forms.

Keywords

• invariant tori
• Neimark-Saker bifurcation
• periodic solution

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