Noise-induced complex dynamics and synchronization in the map-based Chialvo neuron model

The paper considers a stochastic version of the conceptual map-based Chialvo model of neural activity. Firstly, we focus on the parametric zone where this model exhibits mono- and bistability with coexistence of equilibria and oscillatory spiking attractors forming closed invariant curves. Stochastic effects of excitement and generation of bursting are studied both numerically and analytically by confidence ellipses. A phenomenon of the noise-induced transition to chaos in a localized two-parametric zone is discussed. Besides, we also study the phenomenon of synchronization between neurons by using a two-neuron network with a small coupling. In this scenario, we have found critical values of noise for which we obtain a good performance for the synchronization between the neurons of the network. •A stochastic version of the map based Chialvo neuron model is considered.•Stochastic effects of bursting are studied both numerically and analytically.•A noise-induced transition to chaos in a localized two-parametric zone is discussed.•Critical noise values yield an excellent performance for two-neuron synchronization.