Dynamical and topological conditions triggering the spontaneous activation of Izhikevich neuronal networks

Abstract

Understanding the dynamic behavior of neuronal networks in silico is crucial for tackling the analysis of their biological counterparts and making accurate predictions. Of particular importance is determining the structural and dynamical conditions necessary for a neuronal network to activate spontaneously, transitioning from a quiescent ensemble of neurons to a network-wide coherent burst. Drawing from the versatility of the Master Stability Function, we have applied this formalism to a system of coupled neurons described by the Izhikevich model to derive the required conditions for activation. These conditions are expressed as a critical effective coupling gC, grounded in both topology and dynamics, above which the neuronal network will activate. For regular spiking neurons, average connectivity and noise play a significant role in their ability to activate. We have tested these conditions against numerical simulations of in silico networks, including both synthetic topologies and a biologically-realistic spatial network, showing that the theoretical conditions are well satisfied. Our findings indicate that neuronal networks readily meet the criteria for spontaneous activation, and that this capacity is weakly dependent on the microscopic details of the network as long as average connectivity and noise are sufficiently strong.