Abstract: We considered  the Ghostburster system model of a class of weak electric fish neuron cells. Firstly, the equilibrium point of the neuron system was given by numerical calculation method. By analyzing the eigenvalues of the Jacobian matrix near the equilibrium point, the stability and its type near the equilibrium point were analyzed. Secondly, using the Hopf bifurcation existence theory and its analysis method, the direction of the model Hopf bifurcation and the approximate solution and the approximate period of the bifurcation period were given. The  results show that when the system parameters are controlled within a certain range, and the system model produces subcritical Hopf bifurcation, the periodic solution orbit is gradually increased and unstable.  Finally, the numerical simulation results of theoretical analysis were given by using MATLAB and other mathematical software. The parameters of the maximum conductance of potassium ion current of dendritic membrane and the injection current of the cell membrane were selected as the bifurcation parameters, and the dynamic behavior of the system under single parameter changes was investigated.

Key words: Ghostburster neuron system, Hopf bifurcation, equilibrium , point, stability, direction of bifurcation