Can noise help create order? The constructive role of Lévy noise in neural networks

In this paper, we investigate the dynamics of a network of non-locally coupled FitzHugh–Nagumo oscillators influenced by Lévy noise. The behavior of this neural network is examined in the regimes of solitary states and multi-stability, as the random noise parameters are varied. Our findings reveal that noise can enhance order within the system by suppressing solitary nodes and increasing the correlation amongst the oscillators. Furthermore, it is discovered that additive noise can increase the probability of establishing chimera states while reducing the likelihood of other regimes, thereby further enhancing the order in the system. Through these findings, the counterintuitive effect of noise is demonstrated, in which the neural oscillator network entropy decreases despite the introduction of noise fluctuations. We also construct basins of attraction for solitary states, to help understand the effects on the system dynamics due to changes in the Lévy noise parameters. The findings have implications for the constructive use of noise in influencing the dynamics of neural network systems, including those in the brain.