Organic electrochemical devices are an emerging class of devices with synaptic properties that might allow for the implementation of next-generation neuromorphic circuits for power-efficient computing. Here, a brain-inspired neural network approach, namely reservoir computing, which relies on a nonlinear transformation of a low-dimensional input signal onto a high-dimensional output space for information processing is utilized. The implementation of reservoir computing using dendritic networks of polymeric fibers is demonstrated and the nonlinear response of the polymer networks are analyzed and the sources of nonlinearity are identified. Furthermore, by adding a delayed feedback loop to the reservoir, it is proven that such a network can undergo a bifurcation into a chaotic state, proving sufficient complexity of the system for advanced classification tasks with time-dependent data. Ultimately, a classification task is carried out and the accuracy is compared of the classification of different degrees of complexity of the system, showing an increase in accuracy from 60% for the base network to 80% when the delayed feedback loop is incorporated.