Small neural networks under external forcing: Periodic pulses and Lévy noise

Abstract Neurons in an excitable mode do not show spiking activity and therefore do not contribute to the information transfer transmission and its processing. However, some external influences, coupling or time delay can lead to the appearance oscillations in individual systems or networks. In this study, we analyze the dynamics of a small network of locally coupled FitzHugh–Nagumo oscillators in the absence and presence of several types of external influence. Firstly, we consider the impact of periodic-pulse exposure generated as a periodic sequence of Gaussian pulses. Secondly, we show what behavior can be induced by Lévy noise and its special case, white Gaussian noise. For both types of influences, we have identified the appropriate parameters (local coupling strength, intensity, and frequency) that induces spiking activity in a small network.