Experimental datasets of networks of nonlinear oscillators: Structure and dynamics during the path to synchronization

The analysis of the interplay between structural and functional networks require experiments where both the specific structure of the connections between nodes and the time series of the underlying dynamical units are known at the same time. However, real datasets typically contain only one of the two ways (structural or functional) a network can be observed. Here, we provide experimental recordings of the dynamics of 28 nonlinear electronic circuits coupled in 20 different network configurations. For each network, we modify the coupling strength between circuits, going from an incoherent state of the system to a complete synchronization scenario. Time series containing 30000 points are recorded using a data-acquisition card capturing the analogic output of each circuit. The experiment is repeated three times for each network structure allowing to track the path to the synchronized state both at the level of the nodes (with its direct neighbors) and at the whole network. These datasets can be useful to test new metrics to evaluate the coordination between dynamical systems and to investigate to what extent the coupling strength is related to the correlation between functional and structural networks. We provide the times series of N=28 Rössler electronic oscillators for 20 different network configurations (compressed file with tag R1 to R20). For each network structure, we recorded the times series for 101 different coupling strengths between oscillators. Each one of the 101 corresponding files is labeled as ST_X_Y.dat where X is a value between X=0 and X=100 that corresponds, respectively, to the minimum and maximum coupling strength. The value of Y corresponds to the repetition number, which can be 1, 2 of 3 (i.e., we repeated the same experiment three times). Data files contain the second variable of the 28 nodes arranged in columns with a length of 30000 points. In a second file named Structure.zip, all the network structures are given, each file having a name Net_R.dat, where R=1, 2… 20. The degree of each node (i.e., number of output connections) is the same for all network configurations, where the specific neighbors of each node are re-arranged randomly.R.S.E. acknowledges support from Consejo Nacional de Ciencia y Tecnología call SEP-CONACYT/CB-2016-01, grant number 285909 and Universidad de Guadalajara CGA/CIPV/789/2019 "Programa de Concurrencias Financieras para la Investigación y Atención de la Vinculación 2019". J.M.B. acknowledges financial support from MINECO (project FIS2017-84151-P)