The ability to efficiently analyze the activities of biological neural networks can significantly promote our understanding of neural communications and functionalities. However, conventional neural signal analysis approaches need to transmit and store large amounts of raw recording data, followed by extensive processing offline, posing significant challenges to the hardware and preventing real-time analysis and feedback. Here, we demonstrate a memristor-based reservoir computing (RC) system that can potentially analyze neural signals in real-time. We show that the perovskite halide-based memristor can be directly driven by emulated neural spikes, where the memristor state reflects temporal features in the neural spike train. The RC system is successfully used to recognize neural firing patterns, monitor the transition of the firing patterns, and identify neural synchronization states among different neurons. Advanced neuroelectronic systems with such memristor networks can enable efficient neural signal analysis with high spatiotemporal precision, and possibly closed-loop feedback control.