Nonlinear analysis and multiplier-free digital realization of a modified 4D Wilson neural model for real-time neuromorphic applications

In this study, we propose a computationally efficient, multiplier-free digital realization of the four-dimensional Wilson neuron model, a well-established framework for modeling complex neural dynamics. To enable large-scale real-time implementation on digital hardware, we reformulate the nonlinear terms in the model using a hybrid approximation strategy based on power-of-two arithmetic and look-up tables (LUTs), significantly reducing computational complexity while preserving the system’s rich dynamical behavior. This approach leverages advanced optimization techniques to minimize resource usage, making it suitable for Artificial Intelligence applications that require efficient processing of large-scale neural networks. The resulting Digital-Friendly Wilson 4D (DFW4-D) model is validated through several approaches, including numerical error analysis, Lyapunov exponent calculations, and stimulus–response behavior under auditory inputs. The Lyapunov analysis demonstrates that the proposed model retains the stability properties of the original system across a wide range of initial conditions and external currents. Furthermore, extensive FPGA-based synthesis on multiple platforms reveals a drastic improvement in operating frequency—up to 4.8× —with complete elimination of DSP block usage. This work offers a scalable and biologically realistic digital neuron model suitable for neuromorphic signal processing and low-power cognitive computing, with particular implications for embedded biomedical systems and AI-driven applications.