recur - a bilinear recurrent equation

Calling Sequence

[y]=recur(x0,var,k,n)

[integr]=logr(k,var)

Description

computes solutions of a bilinear recurrent equation

x(i+1)=-x(i)*(k + sqrt(var)*br(i))
   

with initial value x0 and driven by a white noise of variance var.

Trajectories are drawn and the empirical Lyapunov exponent is returned ( x(i) is not to much different from exp(y*i) )

A theoretical computation of the Lyapunov exponent is given by

[integr]=logr(k,var)