Non-trivial generation and transmission of information in electronically designed logistic-map networks.

In this work, we carry out a critical analysis of the information generated and transmitted in an electronic implementation of diffusively coupled logistic maps. Our implementation allows one to change the coupling configuration (i.e., the network) and fine-tune the coupling strength and map parameters, but has minimal electronic noise and parameter heterogeneity, which generates collective behaviors that differ from numerical simulations. In particular, we focus on analyzing two dynamical regimes and their dependence on the coupling configuration: one where there is a maximum of information generated and transmitted-corresponding to synchronization of chaotic orbits-and another where information is generated but (practically) not transmitted-corresponding to spatiotemporal chaos. We use Shannon entropy to quantify information generation and mutual information to quantify information transmission. To characterize the two dynamical regimes, we introduce a conditional joint entropy that uses both quantities (entropy and mutual information) and analyze its values for 60 different coupling configurations involving 6 and 12 coupled maps. We find that 90% of the configurations exhibit chaotic synchronization and 92% spatiotemporal chaos, which emerges preceding the chaotic synchronous regime that requires strong coupling strengths. Our results also highlight the coupling configurations that maximize the conditional joint entropy in these regimes without requiring a densely coupled system, which has practical implications (since introducing couplings between units can be costly). Overall, our work contributes to understand the relevance that the network structure has on the generation and transmission of information in complex systems.