Log-domain implementation of complex dynamics reaction-diffusion neural networks

We have identified a second-order reaction-diffusion differential equation able to reproduce through parameter setting different complex spatio-temporal behaviors. We have designed a log-domain hardware that implements the spatially discretized version of the selected reaction-diffusion equation. The logarithmic compression of the state variables allows several decades of variation of these state variables within subthreshold operation of the MOS transistors. Furthermore, as all the equation parameters are implemented as currents, they can be adjusted several decades. As a demonstrator, we have designed a chip containing a linear array of ten second-order dynamics coupled cells. Using this hardware, we have experimentally reproduced two complex spatio-temporal phenomena: the propagation of travelling waves and of trigger waves, as well as isolated oscillatory cells.