Local pacing, noise induced ordered wave in a 2D lattice of neurons

Abstract

Appropriate noise can enhance the regularity in electrical activity of neuron, and stochastic resonance emerges when periodic forcing is imposed on the neuron and/or neuronal network. In this paper, periodic forcing is imposed on some neurons of a two-dimensional square lattice with nearest-neighbor connection (the boundary of one side in the network of neurons), which the local kinetics of node is described by Hindmarsh-Rose neuron, while noise is imposed on another side of the two-dimensional lattice. Indeed, spiral waves can be developed in the side of the network driven by appropriate noise intensity while the another side is occupied by plane wave. A statistical factor of synchronization is defined to discern the occurrence of regularity induced by local noise and local pacing. The emitted plane wave from one side of network can be suppressed by noise and disordered state emerges with stronger noise being used on all nodes of the network, furthermore, spiral wave is induced in the network under appropriate noise intensity. The network shows spatial regularity when spiral wave is developed and it is interesting to find spiral wave can coexist with plane wave in the network. Stochastic resonance-like behavior could be observed in the two-dimensional lattice composed of neurons even if noise and periodic forcing are imposed on different areas of the network. The occurrence of spatial regularity under coherence could rely on the competition between noise driving-induced segments and wave fronts induced by periodic forcing.