Bifurcation and Firing Behavior Analysis of the Tabu Learning Neuron with FPGA Implementation

Neuronal firing behaviors are fundamental to brain information processing, and their abnormalities are closely associated with neurological disorders. This study conducts a comprehensive bifurcation and firing-behavior analysis of an improved Tabu Learning neuron model using a semi-analytical discrete implicit mapping framework. First, a discrete implicit mapping is constructed for the Tabu Learning neuron, enabling high-precision localization of stable and unstable periodic orbits within chaotic regimes and overcoming the limitations of conventional time-domain integration. Second, an eigenvalue-centered analysis is used to classify bifurcation types and stability, summarized in explicit bifurcation tables that reveal self-similar offset bifurcation routes, coexisting periodic and chaotic attractors, and chaotic bubbling firing patterns. Third, the proposed neuron model and its discrete mapping are implemented on an FPGA platform, where hardware experiments faithfully reproduce the analytically predicted stable and unstable motions, thereby tightly linking theoretical analysis and digital neuromorphic hardware. Overall, this work establishes a unified analytical–numerical–hardware framework for exploring complex neuronal dynamics and provides a potential basis for neuromodulation strategies and neuromorphic computing system design.