Abstract
The three-dimensional set of ordinary differential equations, known as the Lorenz equations were first introduced by Ed Lorenz [2] in 1963 as a model of convection in a two-dimensional cell. Since then other authors, e.g. Haken [1] have shown that the same equations can be derived from the Maxwell-Bloch equations for single-mode lasers with damping. The equations are of mathematical interest because of the wide variety of behaviours that they display -- including chaotic behaviour and the existence of strange attractors -- for different values of the three parameters r, σ and b. It seems that the relevant range of parameters for laser applications is σ < b + 1 which, it must be confessed, is not the parameter range of greatest interest from a mathematical point of view. However, providing 3σ - 1 > 2b attracting chaotic behaviour will still occur [3,4] though it will occur at parameter values for which the equations also have stable stationary points and these may determine most of the observed behaviour of the system.
© 1985 Optical Society of America
PDF ArticleMore Like This
N. M. Lawandy, Ali Fahmy, and Kayee Lee
WD11 Instabilities and Dynamics of Lasers and Nonlinear Optical Systems (IDLNOS) 1985
Sarben Sarkar, J S Satchell, and H J Carmichael
THC5 Instabilities and Dynamics of Lasers and Nonlinear Optical Systems (IDLNOS) 1985
N. R. Heckenberg, Tin Win, and C. O. Weiss
ThN6 International Quantum Electronics Conference (IQEC) 1992