Bifurcation evolution, frequency analysis and FPGA implementation in a tabu learning neuron system

The complex dynamical behaviors of neuron models, including bifurcation characteristics and firing patterns, offer important insights for neuroscience research. To study these dynamics, we employ an implicit mapping methodology to investigate the dynamic properties of a Tabu Learning-based neuronal framework. Through advanced analysis, we show that neuronal periodic bifurcations evolve drastically with parameters, transforming from period-doubling into two distinct unstable saddle-node types. Phase and time-series analyses reveal different attractors and diverse firing patterns. To explore the periodic motions from harmonic components, we integrate discrete mapping with Fourier series. This approach provides a quantitative examination of amplitude–frequency characteristics in the context of coexisting bifurcation transitions and firing behaviors, thereby establishing a novel perspective for attractor analysis. Finally, a field-programmable gate array (FPGA) implementation serves as empirical confirmation that the results obtained from the derived solutions are accurate. Overall, this research provides an effective framework for elucidating nonlinear neuronal dynamics and is expected to contribute to advances in brain science and artificial intelligence.