  We investigate the synchronization between two neurons using the stochastic
version of the map-based Chialvo model. To simulate non-identical neurons, a
mismatch is introduced in one of the main parameters of the model.
Subsequently, the synchronization of the neurons is studied as a function of
this mismatch, the noise introduced in the stochastic model, and the coupling
strength between the neurons. We propose the simplest neuron network for study,
as its analysis is more straightforward and does not compromise generality.
Within this network, two nonidentical neuron maps are electrically coupled. In
order to understand if specific behaviors affect the global behavior of the
system, we consider different cases related to the behavior of the neurons
(chaotic or periodic). Furthermore, we study how variations in model parameters
affect the firing frequency in all cases. Additionally, we consider that the
two neurons have both excitatory and inhibitory couplings. Consequently, we
identify critical values of noise and mismatch for achieving satisfactory
synchronization between the neurons in both cases. Finally, we conjecture that
the results are of a general nature and are applicable to different neuron
models.
