  Complex systems in the real world can be modeled as a network of connected
components. The human brain, as a network of neurons among which the
interactions cause perception, is a complex network. Synchronization is a
dynamical phenomenon that can be seen in the brain. The network topology has a
remarkable impact on both the function and the dynamics of neural networks. In
this research, synchronization of neural networks is scrutinized through
creating various topologies. These networks include both excitatory and
inhibitory neurons. We investigate the dynamics of different networks by random
rewiring of the synaptic connections. In this manner, a regular network
transforms into a small-world network and then becomes a random network.
Coherence level which is measured and utilized as the criteria to analyze
synchronicity, experiencing a sharp increase as the network changes into the
small-world network and growing steadily by the end. On the other hand, a
decreasing trend of coherence level is revealed starting from a complete
excitatory network and gradually increasing of inhibitory neurons. Thus, the
coherence level reaches approximately zero in a complete inhibitory network. By
increasing the number of neurons in the network, the degree of synchronization
follows a power-law distribution; however, the number of synaptic connections
of each neuron and their conductance have a positive impact on synchronization.
By applying the model to a C-elegance neural network, not only the mentioned
parameters but also the role of the degree distribution are highlighted.
