Self-organization in autonomous, recurrent, firing-rate CrossNets with quasi-Hebbian plasticity.

We have performed extensive numerical simulations of the autonomous evolution of memristive neuromorphic networks (CrossNets) with the recurrent InBar topology. The synaptic connections were assumed to have the quasi-Hebbian plasticity that may be naturally implemented using a stochastic multiplication technique. When somatic gain g exceeds its critical value g(t), the trivial fixed point of the system becomes unstable, and it enters a self-excitory transient process that eventually leads to a stable static state with equal magnitudes of all the action potentials x(j) and synaptic weights w(jk). However, even in the static state, the spatial distribution of the action potential signs and their correlation with the distribution of initial values x(j)(0) may be rather complicated because of the activation function's nonlinearity. We have quantified such correlation as a function of g, cell connectivity M, and plasticity rate η, for a random distribution of initial values of x(j) and w(jk), by numerical simulation of network dynamics, using a high-performance graphical processing unit system. Most interestingly, the autocorrelation function of action potentials is a nonmonotonic function of g because of a specific competition between self-excitation of the potentials and self-adaptation of synaptic weights.