Networks of dynamical systems are common models for many problems in physics, engineering, chemistry, biology, and social sciences. In particular, the interplay between network structure and synchronization has been extensively studied, as synchronization has been shown to play an important role in the function or dysfunction of a wide spectrum of technological and biological networks. This highly interdisciplinary special issue integrates new research contributions from different areas in applied mathematics, physics, neuroscience, and engineering, including stability and bifurcation theory, information and ergodic theory, averaging methods, and mathematical control theory. It can be roughly divided into three themes. They demonstrate that such variations can lead to the emergence of macroscopic chaos, multi-stability, and final-state uncertainty in the collective behavior of the neuronal network. Analytical techniques are used to identify the asymptotic behavior of the macroscopic mean field dynamics of the network.