Noise-induced synchronization in a lattice Hodgkin-Huxley neural network

We examine how the synchronization of the series of action potentials (APs) of realistic neurons interconnected in a lattice is influenced by variations of both the direction and magnitude of neuron-neuron connectivity in a noisy environment. We first demonstrate the existence of an optimal noise level that brings about the highest average number of APs per unit time, for a single Hodgkin-Huxley neuron. We then show that synchronization, as a collective response of interconnected neurons forming an N×N lattice, is optimal at different noise strengths σc=σc(p), depending on the degree of random-link malfunction parameterized by flipping direction probability p. Thus, even without the scale-free structure of neuronal networks, proper combinations of both randomness in reconnection (flipping) and noisy environment can be beneficial to the collective functioning of neurons.