The Role of Connection Density in an Adaptive Network with Chaotic Units

Abstract: We investigate the role of connection density in an adaptive network model of chaotic units that dynamically rewire based on their internal states and local coherence. By systematically varying the network's connectivity density, we uncover distinct dynamical regimes and structural transitions, revealing mechanisms of spontaneous modularity, dynamical segregation, and integration. We find that at higher densities, the network exhibits both local clustering and global synchrony. Additionally, we observe that low-density networks tend to fragment into desynchronized clusters, while high-density networks converge to synchronized states combining strong global integration with persistent modular segregation. Inspired by neural architectures, our model provides a general framework for understanding how simple microscopic rules can give rise to complex emergent behaviors in dynamical networks.