Breathing oscillations as one of the low frequency, large amplitude discharge instabilities have serious influence on the performance and lifetime of Hall thrusters. In order to acquire a better understanding of the breathing-oscillation in the Hall thrusters and provide the effective suppression methods for breathing-oscillation, the excitation mechanism and influence factors of the breathing oscillations are investigated by utilizing the two-zone predator-prey (P-P) model in this paper. The two-zone P-P model divides the discharge channel of Hall thruster into two parts according to the working principle of Hall thruster: one is the near anode zone and the other e is the ionization zone. The model includes the ion radial diffusion effect and electrons-wall interaction effect. The four-order Range-Kuttle method is utilized to solve the nonlinear two-zone P-P model equation. The research results show that the interaction of electrons with the wall has the inhibition effect on the breathing oscillations caused by the energy consumption due to the colliding with discharge channel wall. However, ion radial diffusion effect which is near anode has an excitation effect on the breathing oscillation. The ion and neutral atom dynamic behaviors obviously show the P-P feature in the phase space. In other words, there is a phase difference between the change of ion density and the change of neutral particle density. Relying on the intensity of the ions radial diffusion effect, the mode oscillation frequency and oscillation amplitude of discharge current present non monotonic change trend. More specifically, with the increase of intensity of ion radial diffusion effect, the oscillation frequency first increases and then decreases. However, the discharge peak current first decreases and then increases. Furthermore, the breathing oscillations excitation is irrelevant to the length of ionization zone, and the oscillation frequency increases (oscillation period) with length of ionization zone increasing (decreasing), provided that the length of discharge channel is constant. The research results of this paper will provide support to make clear the excitation mechanism and propose the new method of suppressing the breathing oscillations in the hall thrusters.