Reinforced Random Walker meets Spike Timing Dependent Plasticity

Abstract

We blended Reinforced Random Walker (RRW) and Spike Timing Dependent Plasticity (STDP) as a minimalistic model to study plasticity of neural network. The model includes walkers which randomly wander on a weighted network. A walker selects a link with a probability proportional to its weight. If the other side of the link is empty, the move succeeds and links weight is strengthened (Long Term Potentiation). If the other side is occupied, then the move fails and the weight of the link is weakened (Long Term Depression). Depending on the number of walkers, we observed two phases: ordered (a few strong loops) and disordered (all links are alike). We detected a phase transition from disorder to order depending on the number of walkers. At the transition point, where there was a balance between potentiation and depression, the system became scale-free and histogram of weights was a power law. This work demonstrate how dynamic of a complex adaptive system can lead to critical behavior in its structure via a STDP-like rule.