This is R code to find by simulation the Lyapunov exponent for a fairly general class of SDE.

The general methods follow those described in: Approximation of Upper Lyapunov Exponents of Bilinear Stochastic Differential Systems by Denis Talay SIAM Journal on Numerical Analysis 28(4):1141--1164 (1991) http://www.jstor.org/stable/2157791

with the addition of an "exponential method", appropriate for a more restricted class.

For some details on the methods, see simulation-description.pdf.

Mostly this code is to support the paper: Stochastic population growth in spatially heterogeneous environments to appear in JMB, by Steven N. Evans, Peter L. Ralph, Sebastian J. Schreiber, Arnab Sen http://arxiv.org/abs/1105.2280

and is not currently being used. Let the user beware? If it's useful for you though, let me know.

What is here: Lyapunov-approx-fns.R -- the functions that do the work Lyap-check.R -- provides some plots to check what we're doing is working Lyapunov-approx.R -- compares the three methods from Talay's paper exploration.R -- contains code to make the figures in the paper.