Functional magnetic resonance imaging (fMRI) is a technique that is sensitive to correlates of neuronal activity. The application of fMRI to measure functional connectivity of related brain regions across hemispheres (e.g. left and right motor cortices) has great potential for revealing fundamental physiological brain processes. Primarily, functional connectivity has been characterized by linear correlations in resting-state data, which may not provide a complete description of its temporal properties. In this work, we broaden the measure of functional connectivity to study not only linear correlations, but also those arising from deterministic, non-linear dynamics. Here the delta-epsilon approach is extended and applied to fMRI time series. The method of delays is used to reconstruct the joint system defined by a reference pixel and a candidate pixel. The crux of this technique relies on determining whether the candidate pixel provides additional information concerning the time evolution of the reference. As in many correlation-based connectivity studies, we fix the reference pixel. Every brain location is then used as a candidate pixel to estimate the spatial pattern of deterministic coupling with the reference. Our results indicate that measured connectivity is often emphasized in the motor cortex contra-lateral to the reference pixel, demonstrating the suitability of this approach for functional connectivity studies. In addition, discrepancies with traditional correlation analysis provide initial evidence for non-linear dynamical properties of resting-state fMRI data. Consequently, the non-linear characterization provided from our approach may provide a more complete description of the underlying physiology and brain function measured by this type of data.