Abstract

In the real world we typically have very few observations from a spatially and temporally extended system. This is true in the study of climate, ecology and plasma physics. Here we investigate how having limited measurements from a simple flocking system effects the measured behaviour of that system. We show that mutual information provides a robust measurement of the behaviour of the system even when we only track very few of the particles in the flock. We then show an example using mutual information and cross correlation to measure correlation in the turbulent plasma of the solar wind. We find that the correlation length in the solar wind changes with the solar cycle. This is relevant to the study of modulation of cosmic ray flux and magnetospheric substorm size and frequency.