The goal of our research group is to understand how biological networks generate patterns of activity with an emphasis on oscillatory networks, how these networks process information and perform computations, and how all of this depends on the dynamic properties of the participating nodes, the connectivity and the network topology. We particularly focus on oscillatory networks of the nervous system, which play important roles in cognition and motor behavior both in health and disease. We develop and use mathematical modeling, numerical simulations, dynamical systems tools, parameter estimation and inference algorithms, and we have a well-developed network of collaborations with experimental scientists carrying out research both in vitro and in vivo. Our research includes the investigation of the mechanisms of selection of frequencies, amplitudes and additional activity attributes of the experimentally observed patterns, and the network response to external, often oscillatory signals, that are subject to background noise inputs (e.g., resonances, entrainment, correlations) as the result of the interplay of nonlinearities, time scales and the levels of neuronal organization (cellular, synaptic, micro-, meso- and macrocircuit). This research extends to biological networks in the context of chemistry and systems biology (e.g., biochemical, genetic). Our efforts also include the investigation of the relationship between experimental and observable data to models in collaboration with statistical neuroscientists and data scientists. These projects include of identification of degeneracy (multiple biological scenarios producing the same observable patterns) and the resolution of the associated problem of unidentifiability in models and data (the lack of ability to uniquely estimate model parameters from observable data). They also include the determination of dynamic scenarios underlying correlations and causal rules in neuroscience data.