An optically-injected semiconductor laser exhibits chaotic behaviour for certain values of the parameters. The underlying model is an example of a general three-dimensional system of ordinary differential equations, and existing analyses agree very well with experiments. We outline a method for computing an approximate but powerful description of the behaviour in the chaotic regime in terms of symbolic dynamics. The method is based on computing the stable and unstable manifolds of the system, which can then be used to give a natural description of the orbits.
|Unpublished - 2003
Additional information: Later published in EQUADIFF: Proceedings of the International Conference on Differential Equations, by World Scientific Publishing (2005), pp. 871-876, ISBN 9812561692
Sponsorship: The work of Collins was partially supported by Leverhulme Special Research Fellowship SRF/4/9900172. The work of Krauskopf was partially supported by an EPSRC Advanced Research Fellowship.