Dynamical properties and synchronization of complex non-linear equations for detuned lasers

Gamal M. Mahmoud, T. Bountis, M. A. Al-Kashif, Shaban A. Aly

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

We study the dynamics and synchronization properties of a system of complex non-linear equations describing detuned lasers. These equations possess a whole circle of fixed points, while the corresponding real variable equations have only isolated fixed points. We examine the stability of their equilibrium points and determine conditions under which the complex equations have positive, negative or zero Lyapunov exponents and chaotic, quasiperiodic or periodic attractors for a wide range of parameter values. We investigate the synchronization of chaotic solutions of our detuned laser system, using as a drive a similar set of equations and applying the method of global synchronization. We find attractors whose three-dimensional projection is not at all similar to the well-known shape of the (real) Lorenz attractor. Finally, we apply complex periodic driving to the electric field equation and show that the model can exhibit a transition from chaotic to quasiperiodic oscillations. This leads us to the discovery of an exact periodic solution, whose amplitude and frequency depend on the parameters of the system. Since this solution is stable for a wide range of parameter values, it may be used to control the system by entraining it with the applied periodic forcing.

Original languageEnglish
Pages (from-to)63-79
Number of pages17
JournalDynamical Systems
Volume24
Issue number1
DOIs
Publication statusPublished - Mar 2009
Externally publishedYes

Fingerprint

Nonlinear equations
Synchronization
Nonlinear Equations
Laser
Lasers
Real variables
Attractor
Fixed point
Lorenz attractor
Global Synchronization
Periodic Forcing
Electric fields
Stability of Equilibria
Equilibrium Point
Lyapunov Exponent
Range of data
Electric Field
Periodic Solution
Circle
Projection

Keywords

  • Attractors
  • Chaos
  • Control
  • Detuned laser systems
  • Periodic forcing
  • Synchronization

ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science Applications

Cite this

Dynamical properties and synchronization of complex non-linear equations for detuned lasers. / M. Mahmoud, Gamal; Bountis, T.; Al-Kashif, M. A.; Aly, Shaban A.

In: Dynamical Systems, Vol. 24, No. 1, 03.2009, p. 63-79.

Research output: Contribution to journalArticle

M. Mahmoud, Gamal ; Bountis, T. ; Al-Kashif, M. A. ; Aly, Shaban A. / Dynamical properties and synchronization of complex non-linear equations for detuned lasers. In: Dynamical Systems. 2009 ; Vol. 24, No. 1. pp. 63-79.
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