Simple model of complex bursting dynamics in developing networks of neuronal cultures

We consider and analyse emergence of spatiotemporal activity patterns in living neuronal cultures. Such patterns are often referred to as neuronal avalanches exemplifying self-organized criticality in living systems. A crucial question is how these patterns can be explained and modelled in a way that is mathematically tractable and yet broad enough to account for neuronal heterogeneity and complexity. Here we propose and analyse a simple model that may constitute a response to this question. A distinctive feature of the model is an energy feedback regulating efficacy of local neural connectivity. Such regulatory mechanism steers the overall dynamics to that of balancing on the edge of network percolation transition. Network activity in this state exhibits population bursts satisfying the scaling avalanche conditions. This network state is self-sustainable and represents an energetic balance between global network-wide processes and spontaneous activity of individual elements.