Controlling spatiotemporal dynamics of neural networks by Lévy noise

Abstract

We explore numerically how additive Lévy noise influences the spatiotemporal dynamics of a neural network of nonlocally coupled FitzHugh–Nagumo oscillators. Without noise, the network can exhibit various partial or cluster synchronization patterns, such as chimera and solitary states, which can also coexist in the network for certain values of the control parameters. Our studies show that these structures demonstrate different responses to additive Lévy noise and, thus, the dynamics of the neural network can be effectively controlled by varying the scale parameter and the stability index of Lévy noise. Specifically, introducing Lévy noise in the multistability mode can increase the probability of observing chimera states while suppressing solitary states. Nonetheless, decreasing the stability parameter enables one to diminish the noise effect on chimera states and amplify it on solitary states.