From nonlinear neuronal dynamics to AI-optimized VLSI hardware: multiplier-free FPGA implementation of memristive FN-HR coupled neural networks for intelligent systems

This paper proposes an innovative approach to translating the nonlinear dynamics of a memristive FitzHugh-Nagumo-Hindmarsh-Rose (FN-HR) coupled neuron model into an AI-optimized, resource-efficient VLSI implementation on FPGA platforms, advancing intelligent computing paradigms. The bidirectional memristive synapse coupling FN and HR neurons enables rich dynamic behaviors such as mixed-mode oscillations and chaos, which are harnessed to enhance adaptive machine learning and neural network training. A detailed dynamical analysis, including Lyapunov exponent spectra and synchronization properties, identifies parameter regimes suitable for AI applications. Nonlinear operators are approximated using quantized lookup tables and three-term sinusoidal expansions, achieving RMSE values of 0.0105 (FN) and 0.0114 (HR) while eliminating DSP usage. Synthesized on an AMD Zynq UltraScale+ ZCU104 FPGA, a 50-neuron network utilizes 5.3% LUTs and 7% BRAM, delivering 42 million neuron-updates per second at 210 mW. This work establishes a scalable, low-power platform for real-time AI-driven neuromorphic computing and intelligent adaptive control systems.