Theory of Nets with Constant or Dynamic Synapses

The experimental observation of the presence and duration of partitions and pulse patterns, respectively, is one alternative to achieve the characterisation of a stationary frequency of distribution. For larger networks, however, the simulation time exceeds our human patience, hence a theoretic coverage is necessary. As the constant synapses form a special case, the development of a generic theory of nets with dynamic synapses becomes necessary. To this end we will introduce the idea of the signal energy and show that the signal equations as well as the entropy are derivable from it. This way the state trajectories of a net can be obtained by theory, for example as the dependency of the entropy on the input pulses. The theory developed here holds for arbitrary input signals (> 0), but pulses of amplitude x and duration td only. The reason for the latter restriction is the much more complicated calculations that would be required, and for the purposes of this book, it would not add anything regarding pulse signals in the treatment of image recognition tasks.