Appendix

Simulator for Chapters 3, 4

The analytical model describing the macrodynamic behavior of the pulse coupled neurons was implemented in a C/C++ simulator.

The major focus for the implementation was an easy-to-understand and maintain source code. There are certainly several options to optimize run time and memory consumption. However, as the theory to describe the behavior of the pulse-coupled neurons was developed over a longer time span, the ease of maintenance was the primary criterion for the implementation. The reader of this book is welcome to reuse parts of the source code or the complete package in his own simulations.

For many simulations in this book, fully connected neurons were used, without back coupling to the neuron itself. In this case the amount of required memory to store the weights between the neurons expands quadratically with the number of neurons. When calculating the analytical model of the neuron behavior, there is an additional problem: For n neurons there exist 2ⁿ possible firing patterns, which means the required memory grows exponentially with the number of neurons. Assuming the likelihood of a firing pattern is stored in a float value of 4 Byte, we would need, for instance, 4 GByte to store the firing patterns of a net with 30 neurons. Certainly one might use hard disk space to store the firing patterns, or apply other tricks. However, this usually leads to increased calculation time, and only moderately increases the number of neurons.