Dynamical consistency in networks of nonlinear oscillators

We investigate, numerically and experimentally, the phenomenon of dynamical consistency in a network of nonlinear oscillators. Dynamical consistency is defined as the ability of a dynamical system to respond in the same way when it is perturbed by the same external signal. This property, fulfilled by specific dynamical systems, has been mainly studied in single oscillators (e.g., lasers or electronic circuits), but just a few works have focused on dynamical systems connected through a non-regular network. Using an electronic array, we can connect a series of nonlinear (analog) electronic circuits to create complex networks, where nodes are coupled between them in a given structure, and an external signal can also be introduced into each particular circuit. Furthermore, the strength of the connections is re-configurable. Next, we analyze the consequences of varying the network's coupling strength and investigate how synchronization and consistency of the whole ensemble arise. Variations in both coupling strengths, i.e. (i) between oscillators and (ii) with the external signal, show the existence of a region where electronic oscillators can respond in the same way to an external perturbation even though they are not completely synchronized with the external signal. We use the Pearson correlation coefficient to measure the consistency of the network, which is characterized by a high correlation between the network output signals and, at the same time, a low correlation with the input signal.