Implementation of Electrically and Chemically Coupled Hindmarsh–Rose Neurons on FPGA Using Backstepping and Lyapunov Control Methods

This study presents the hardware implementation of two coupled Hindmarsh–Rose neuron models with both electrical and chemical coupling on a Field Programmable Gate Array (FPGA). To achieve synchronization between the neurons, Lyapunov and backstepping control methods are applied and analyzed comparatively, along with uncontrolled cases to observe the natural behavior of the coupled neurons. Electrical coupling is modeled using a linear diffusion term, whereas chemical coupling is represented by a nonlinear sigmoid synaptic function adapted for FPGA implementation using a piecewise-linear approximation. The design is realized on a Xilinx XUPV5-XC5VLX110T evaluation board using the VHDL language. All neuron, coupling, and control computations are performed in parallel, exploiting the reconfigurable architecture of the FPGA. The obtained results are compared with MATLAB simulations through both visual analysis and quantitative performance metrics such as root mean square error and relative error. Additionally, hardware metrics including slice utilization, latency, and throughput are evaluated. The results show that the proposed FPGA design achieves accurate synchronization with low latency, demonstrating the feasibility of real-time and neuromorphic applications. Notably, this work reports for the first time the FPGA realization of chemically coupled Hindmarsh–Rose neurons synchronized via the backstepping control method.