  The cooperative behavior of neurons and neuronal areas associated with the
synchronization behavior proves to be a fundamental neural mechanism. In
addition, abnormal levels of synchronization have been related to unhealthy
neural behaviors. Throughout this thesis, it is explored different
synchronization phenomena which emerge through the collective dynamics of
models of neurons coupled in a network. Firstly, it is shown a strong
correlation between the individual dynamics of the neuron with the global
behavior of the synchronization, in which the periodicity seen in the isolated
neuron is reflected in a phase synchronization in the weak coupling region.
Secondly, it is studied the role of bistability in the synchronization of a
network of identical neurons coupled through a mean-field scheme. It is shown
that the simple existence of two distinct stable states can lead the network to
different states of synchronization, depending on the initialization of the
system. Lastly, it is investigated the mechanism for explosive synchronization
of a complex neural network composed of non-identical neurons. The presence of
this regime is accompanied by a hysteresis loop on the network dynamics as the
coupling parameter is adiabatically increased and decreased. It is shown that
the abrupt synchronization transitions are associated with routes to chaos. The
dynamical mechanisms for the bistability region, are given in terms of a
saddle-node bifurcation and a boundary crisis. Therefore, the results of this
thesis show a richness of synchronization behaviors associated with small
changes of the neuronal dynamics bringing new insights to the theoretical study
of neural networks.
