Oscillation propagation in neural networks with different topologies

In light of the issue of oscillation propagation in neural networks, various topologies of FitzHugh-Nagumo neuron populations are investigated. External Gaussian white noise is injected into the first neuron only. Before the oscillation spreads to the other neurons in the network, some of the inherent stochasticity within the noise-induced oscillation of the first neuron is filtered out due to the neuron's nonlinear dynamics. Both the temporal and the spatial coherence of the evoked activity's propagation are analyzed in conjunction with the network topology randomness p, the coupling strength between neurons g, and the noise amplitude D. The temporal periodicity of the global neural network presents a typical coherence biresonance (CBR) characteristic with regard to the noise intensity. The network topology randomness exerts different influences on the resonance effects for different coupling strength regimes. At an intermediate coupling strength, the random shortcuts reinforce the interactions between the neurons, and then more stochasticity in the firings of the first neuron spreads within the network. Consequently, CBR is decreased with the increase of the network topology randomness. At a large coupling strength, the random shortcuts assist the nonlinearity in impairing the stochastic components, and consequently help to enhance the resonance effects, which differed significantly from previous related work. However, the degree of the spatial synchronization of the systems increases monotonically as the network topology randomness increases at any coupling strength.