**3.3 Linear differential equations and recurrent neural networks**

With respect to their dynamical properties, recurrent neural networks may be described as showing fixed point attractors. How is it possible to design a neural network with specific dynamics? Dynamical systems are often described by differential equations. In such cases the construction of a recurrent network is easily possible: Any system described by a linear differential equation of order n can be transformed into a recurrent neural network containing n units (Nauck et al., 2003). To this end, the differential equation has first to be transferred into a system of n coupled differential equations of the order one.
