In the brain, synchronized activity of neurons is essential for the development and computation. Synchronization in NoNs and modular networks has been explored theoretically based several models, including phase oscillators (Arenas et al., 2006, 2008; Barreto et al., 2008; Laing, 2009; Zhao et al., 2010; Louzada et al., 2013), chaotic oscillators (Zhao et al., 2011; Aguirre et al., 2014; Leyva et al., 2017), and various neuron models (Zhao et al., 2010; Batista et al., 2012; Prado et al., 2014), especially from the viewpoint of competition of global and local synchronizations depending on the ratio or the strength of interactions within and between the subnetworks. In a system of heterogeneous phase oscillators, Arenas et al. (2006) studied the dynamical stability of a locally synchronized state in hierarchically modular networks and provided analytical support based on the master stability function. Zhao et al. (2010) used a similar phase oscillator system to investigate the effect of modular topology on network dynamics, focusing on the relationship between the degree of topological modularization and the complexity of network dynamics. The case of globally coupled NoNs
