So I am studying chaotic dynamical systems and I need to find mutual information between two chaotic time series say x(t) and y(t). Any help would be much appreciated.
Not sure what you mean by "mutual information". Since they are both chaotic, I assume that you are looking for their cross correlation. The cross correlation is a series of numbers, ci, i=0, ±1, ±2, ±3, ...., that are the correlations between xj and yj+i. If there is a linear combination of cross correlations that is statistically significant, then the two series are probably related in some way. There are software statistical packages that you can use to obtain the cross correlations.
Sorry. It sounds like you are really talking about information theory of chaotic systems. I have no knowledge on the subject.Actually finding correlation would only help us find any linear correlations but chaotic time series means non-linear correlations as well. For that we need to calculate the mutual information.