Evolution of pitchfork bifurcation in a tabu learning neuron model and its application in image encryption

This paper focus on studying the two-dimensional tabu learning neurons in conjunction with applied currents using phase, bifurcation, eigenvalues and sequence diagrams by semi-analytical method. The result demonstrates that neurons under the influence of different amplitudes can exhibit multi-periodic coexisting attractors. Two special kinds of bifurcation are investigated in depth through the analysis of orbit motions. The accurate tracking of neural spike events through phase diagrams is feasible. This paper also demonstrates the coexistence of steady and unsteady firing patterns, which cannot be obtained by the conventional numerical method. In addition, the correctness of the obtained results is verified by means of field programmable gate array. Lastly, the sequences generated by unsteady motions in the system are combined with DNA image encryption, enhancing the security for image encryption.