Experimental observations of cluster synchronization in a biologically inspired neuronal network of chaotic electronic oscillators

This study investigates the emergence of cluster synchronization in a biologically inspired neuronal network composed of 59 coupled chaotic electronic oscillators that is modeled after a dissociated rat cortical culture. A recently introduced spectral block method is employed to predict the formation and sequence of synchronization clusters based solely on the network's structural connectivity, although the exact transition points depend on the values at which the master stability function changes sign. The analysis is conducted through numerical simulations of Rössler oscillators, which allow for a controlled numerical investigation, followed by a second part devoted to the experimental study of a circuit board composed of single-transistor chaotic oscillators. In both cases, the results confirm the expected hierarchical dynamical transition from incoherence to global synchronization via an intermediate cluster state. Furthermore, the analysis of the network of single-transistor chaotic units provides the first experimental validation of the spectral block method and demonstrates that cluster synchronization arises naturally in networks without intentionally designed symmetries. The experimental platform, which features a scalable and reconfigurable electronic network, thus bridges theoretical predictions and real-world observations, highlighting the robustness of cluster synchronization in the presence of nonidealities, noise, and parameter variations, while also emphasizing the practical considerations required when applying the method to real experiments, such as robust cluster identification and calibration of the critical points of the master stability function. These findings advance our understanding of self-organized synchronization in complex systems and have important implications for neuroscience, adaptive computing, and network engineering.