Parkinson's Disease (PD) is currently the second most common neurodegenerative disease. One of the most characteristic symptoms of PD is resting tremor. Local Field Potentials (LFPs) have been widely studied to investigate deviations from the typical patterns of healthy brain activity. However, the inherent dynamics of the Sub-Thalamic Nucleus (STN) LFPs and their spatiotemporal dynamics have not been well characterized. In this work, we study the non-linear dynamical behaviour of STN-LFPs of Parkinsonian patients using ε -recurrence networks. RNs are a non-linear analysis tool that encodes the geometric information of the underlying system, which can be characterised (for example, using graph theoretical measures) to extract information on the geometric properties of the attractor. Results show that the activity of the STN becomes more non-linear during the tremor episodes and that ε -recurrence network analysis is a suitable method to distinguish the transitions between movement conditions, anticipating the onset of the tremor, with the potential for application in a demand-driven deep brain stimulation system.