Spontaneous dynamical differentiation in an experimental network of single-transistor chaotic oscillators modeling a biological neuronal culture

The role of structural connectivity in complex network dynamics is a significant interdisciplinary concern and a central topic in neuroscience. Although synchronization phenomena have been thoroughly studied in terms of the macroscopic properties that it generates, how the structural connections affect the local behavior of the nodes, such as brain regions, remains less clearly understood. Electronic chaotic oscillators have been suggested as possible experimental analogs of other natural and artificial nonlinear systems, allowing such issues to be addressed in physical experiments. However, to date, only simple network topologies, e.g., rings, have been used systematically as substrates for exploring pattern formation. Here, we present an experiment wherein a large network of single-transistor chaotic oscillators was obtained from a mesoscopic model of a real biological culture of neurons plated after being mechanically separated. The network conjointly featured a marked node degree heterogeneity and a small-world organization. After detailed circuit-level simulations, the network was realized on a high-density printed circuit board. Its dynamical behavior was investigated by performing bidimensional sweeps of voltages controlling the coupling strengths and node dynamics at a global level, that is, varying in unison the intensity of all links in the fixed network topology, while sweeping the control parameter of all nodes simultaneously. A rich interplay was found between structural connectivity, synchronization, and node dynamics, where nodes with high degree were found to have the propensity to generate more complex and symmetric signals under strong coupling. Remarkably, information-theoretic analyses revealed the formation of functional dependencies in the form of asymmetric information flows among the symmetrically connected nodes, demonstrating the breaking of the symmetries of the structural couplings and establishment of directed relationships depending on the node degree in diverse forms. These results were then generalized to simulations of parametrically identical Rössler systems. This study provides compelling experimental evidence that a predetermined physical network based on elementary electronic entities can generate highly heterogeneous functional patterns. The electronic setup, whose design materials are fully provided, offers a versatile platform for future research into the formation of synchronized clusters, high-order interactions, and the impact of lesions.