Chaotic dynamics and synchronization under tripartite couplings: Analyses and experiments using single-transistor oscillators as metaphors of neural dynamics

This study addresses, from the perspective of an elementary electronic model, the synchronization and dynamics of systems where traditional bipartite (pairwise) interaction models are inadequate, such as tripartite synapses and thalamocortical modulation in the human brain. The model under consideration consists of a triplet of single-transistor chaotic oscillators endowed with tripartite couplings, where all pairwise interactions are also subject to modulation by a third node. Through detailed circuit simulations and experiments, it was found that the high-order interactions profoundly shape the dynamics, promoting the onset of chaos and complex mutual interdependence. Recordings performed by sweeping the intensities of the bipartite and tripartite couplings in the presence of strongly parametrically heterogeneous nodes and profound non-idealities revealed that the influence of the coupling scheme can result in a partly generalizable effect. Further insights into directed interdependencies were obtained by applying information-theoretical approaches. Additional simulations of a triplet of parametrically identical Rössler systems confirmed the generality of the experimental results and underlined that tripartite couplings could give rise to complex behaviors, including multistability, that do not arise when only bipartite couplings are present. A simplified stability analysis was also performed to illustrate a semi-analytical approach. These results motivate future experimental work focusing on tripartite couplings in other connection topologies and complex networks, exploring beyond graph-based models of collective dynamics.