Real-Time recurrence plot and quantification analysis on FPGA for embedded nonlinear dynamics

Recurrence plots (RPs) and recurrence quantification analysis (RQA) are powerful tools for analysing the temporal behaviour of dynamical systems, but their high computational cost limits their use in real-time or resource-constrained environments. Existing GPU-accelerated software reduces offline processing time but still require large memory and energy budgets, which limits the application in embedded or streaming environments. This work presents a fully pipelined FPGA architecture that computes recurrence flags and extracts standard RQA metrics directly in hardware. Phase-space vectors are generated in streaming form using a compact circular buffer, while pairwise distances are evaluated using parallel comparison lanes with deterministic cycle-level latency. A multi-bank vector memory organisation is proposed to realise scalable parallelism to improve throughput, and core RQA measures are computed directly in hardware based on on-chip accumulators. Benchmark results indicate that the designed FPGA system delivers over ten times speedup compared to conventional CPU-based methods without precision loss. The system establishes a real-time RP framework for embedded and distributed sensing applications, including biomedical monitoring, vibration and acoustic sensing for infrastructure and network monitoring, environmental and ecological observation using distributed sensors, and underwater monitoring of marine environments.