  Using the machine learning approach known as reservoir computing, it is
possible to train one dynamical system to emulate another. We show that such
trained reservoir computers reproduce the properties of the attractor of the
chaotic system sufficiently well to exhibit chaos synchronisation. That is, the
trained reservoir computer, weakly driven by the chaotic system, will
synchronise with the chaotic system. Conversely, the chaotic system, weakly
driven by a trained reservoir computer, will synchronise with the reservoir
computer. We illustrate this behaviour on the Mackey-Glass and Lorenz systems.
We then show that trained reservoir computers can be used to crack chaos based
cryptography and illustrate this on a chaos cryptosystem based on the
Mackey-Glass system. We conclude by discussing why reservoir computers are so
good at emulating chaotic systems.
