Less is different: why sparse networks with inhibition differ from complete graphs

In neuronal systems, inhibition contributes to stabilizing dynamics and regulating pattern formation. Through developing mean field theories of neuronal models, using complete graph networks, inhibition is commonly viewed as one control parameter of the system, promoting an absorbing phase transition. Here, we show that for sparse networks, inhibition weight is not a control parameter of the transition. We present analytical and simulation results using stochastic integrate and fire neurons. We also give a simple explanation about why the inhibition role depends on topology, even when the topology has dimensionality greater than the critical one. Thus, the generality of neuronal systems mean-field results presented in the literature should be reanalyzed with care.Comment: 5 pages, 4 figures, lette