Cortical activity is characterized by oscillatory dynamics at many scales. To capture such dynamics in a computational model and elucidate on its putative functional roles, we simulated recurrent networks consisting of coupled damped harmonic oscillators (DHOs), so called HORNs. In HORNs, each DHO node represents the aggregate activity of a recurrently connected E-I circuit such as a cortical column. Mathematically, a DHO is given by a 2nd order ordinary differential equation with a single state variable x (amplitude) To model different intrinsic properties of an underlying E-I circuit's recurrent dynamics, we introduce feedback parameters v and w to each DHO, acting on its amplitude and velocity, respectively. Here, we study the influence of these feedback connections on single node dynamics using dynamical systems theory. We performed a bifurcation analysis of DHO dynamics in the (v,w) parameter space and found that nodes undergo a Z(2) symmetric Takens-Bogdanov bifurcation (figure, left). We also found that the feedback parameters v and w influence the node's gain curves G, assessed by driving nodes with harmonic inputs (figure, right a,b), where G is the ratio between the input and the node stationary amplitudes (G>1 indicates amplification). Our analysis shows that feedback connections enable nodes to shift their gain curves, allowing them to perform resonance-based feature-extraction (figure, right, c,d). We also observe that, in general, feedbacks mechanisms enrich DHO nodes dynamics. Such enriched dynamics strengthen the ability of nodes to better separate temporally organized inputs, improving the overall computational performance of a HORN.