Limit cycles of a bineuronal network model (Q1197517)

In this interesting self-contained paper the authors consider a system of two interconnected pacemakers described mathematically as leaky integrators reciprocally connected by synapses which determine a sudden change in the potential of the post-synaptic neuron. The coupled pacemakers may be inhibitory or noninhibitory. The second case is more tractable analytically and the authors prove several results: noninhibitory systems exhibit a periodic behavior, the number of limit cycles is finite and at most two binary codes defined by the neuron discharges exist. The conclusion is that a bineuronal pacemaker system can act as a stable memory. The inhibitory system can have two mutually exclusive alternatives of behavior.