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

Abstract

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 C₁₂ 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 C₁₂ 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 C₁₂, while the pulses from cell #6 decrease C₁₂. 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 C₁₂ increases stepwise, which is the “Hebb mode”, (ii) the C₁₂ decreases stepwise, which is the “anti-Hebb mode”, and (iii) the C₁₂ remains almost unchanged within some small adjustable range, which is the meander mode. The ability to tune the C₁₂via “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.