Dynamical analysis of a tabu learning neuron through the discrete implicit mapping method

Abstract

The complex dynamics of neuron model including bifurcation behaviors and firing patterns, especially unstable firing patterns, furnish a favorable point of view for the research of neurons, which may be of great importance in the prevention of brain-based diseases. To study this issue in depth, the discrete implicit mapping method is employed to evaluate a tabu learning neuron system, which is coupled with electromagnetic excitation and applied driving current in this paper. The bifurcation orbits of periodic motion with rich dynamic phenomena are accurately shown with varying the amplitudes of external input. The evolutions of period-5 to period-20 and period-6 to period-12 can be obtained via period doubling bifurcations and saddle bifurcation. The subcritical pitchfork bifurcation is also exhibited through the complex coexistence behavior of stable and unstable periodic orbits in such a model, which cannot be obtained by the traditional numerical method due to its accumulative errors. The corresponding stabilities and bifurcation of the periodic motions are determined by means of eigenvalues. Therefore, using such a method, the neural spiking events can be developed through phase diagram and time history of membrane potential. Moreover, the tabu learning system is implemented via FPGA (i.e., field programmable gate array), and the unstable and stable phase diagrams are observed completely from oscilloscope, where the experiments results verify the feasibility of semi-analytical solutions. Such investigation will also benefit the development of artificial intelligence and the advances in Brain Medicine.