Emergent Synchronization and Critical Dynamics of Coupled Neurons on Scale-Free Networks Using Chialvo Maps and Domany–Kinzel Cellular Automata

Understanding collective dynamics in heterogeneous neuronal networks is important for characterizing synchronization and critical behavior in complex systems. This paper investigates neuronal dynamics on scale-free networks using the Chialvo neuron map and the Domany–Kinzel (DK) cellular automaton. A Barabási–Albert (BA) scale-free network is generated through preferential attachment to represent heterogeneous neuronal connectivity. A 10,000-node network is used as a common topology for both models. Neuronal synchronization is quantified using a time-averaged synchronization error under degree-normalized diffusive coupling, while stochastic critical behavior is evaluated through stationary activity density over the (p1,p2) parameter space. The results demonstrate a coupling-dependent transition toward synchronized neuronal dynamics and reveal distinct stochastic activity regimes governed by the combined influence of p1 and p2. Comparison with a random network further demonstrates the influence of heterogeneous connectivity on collective dynamics. Overall, the framework provides a unified basis for investigating deterministic synchronization and stochastic critical dynamics on heterogeneous networks.