Cooperation in Neural Systems: Bridging Complexity and Periodicity

Inverse power law distributions are generally interpreted as a manifestation of complexity, and waiting time distributions with power index \mu < 2 reflect the occurrence of ergodicity breaking renewal events. In this Letter we show how to combine these properties with the apparently foreign clocklike nature of biological processes. We use a two-dimensional regular network of leaky integrate-and-fire neurons, each of which is linked to its four nearest neighbors, to show that both complexity and periodicity are generated by locality breakdown: links of increasing strength have the effect of turning local into long-range interaction, thereby generating first time complexity and then time periodicity. Increasing the density of neuron firings reduces the influence of periodicity thus creating a cooperation-induced distinctly non-Poisson renewal condition.