Implementation of Hebb's rules in a network of excitable chemical cells coupled by pulses.

A network of four excitable cells with the Belousov-Zhabotinsky (BZ) reaction is considered both theoretically and experimentally. All cells are coupled by pulses with time delays τ nj between the moment of a spike in cell # n and the moment of the corresponding perturbation of an addressee (cell # j ). The coupling strengths of all connections except the coupling strength C 12 between cells #1 and #2 are constant. Cell #1 is periodically perturbed (with period T ex ) and sends pulses to cell #2. The value of C 12 is controlled by pulses from two other cells (with indexes #5 and #6; cells with indexes #3 and #4 are absent in the considered network), provided the pulses from cell #5 increase C 12 , while the pulses from cell #6 decrease C 12 . Cells #5 and #6 are mutually coupled by inhibitory pulses. Depending on the relations between the values of τ nj , there are three dynamic modes in the network: (i) the coupling strength C 12 increases stepwise, which is the "Hebb mode", (ii) the C 12 decreases stepwise, which is the "anti-Hebb mode", and (iii) the C 12 remains almost unchanged within some small adjustable range, which is the meander mode. The ability to tune the C 12 via "Hebb" and "anti-Hebb" modes introduces memory in the chemical network and, consequently, a mechanism of learning can be realized. The theoretical network is implemented experimentally using four microcells with the BZ reaction provided the pulse coupling between microcells is realized using optical links.