Breathing oscillations as one of the low frequency, large amplitude discharge instabilities have the serious influence on the performance and lifetime of Hall thrusters. In order to acquire a better understanding 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 have been investigated by utilize the two-zone predator-prey (P-P) model in this paper. The two-zone P-P model divide the discharge channel of Hall thruster into two parts according to the working principle of Hall thruster, one of is called the near anode zone, another one is called the ionization zone. The model include the ion radial diffusion effect and of 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, since the energy consumption due to the colliding with discharge channel wall. However, ion radial diffusion effect which in the near anode zone has the excitation effect on the breathing oscillations. The ions and neutral atom dynamics behavior appears obviously P-P feature in the phase space. In other words, there is a phase difference between ions density and neutral particle density variation. Relay on the strength of the ions radial diffusion effect, the mode oscillation frequency and oscillation amplitude of discharge current present non monotonic change tendency. More specifically, with strength of ions radial diffusion effect increases, the oscillation frequency increasing at first and then decreasing. However, the discharge peak current decreasing at first and then increasing. 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), when the length of discharge channel is constant. The research results of this paper will provide support to make clear of the excitation mechanism and propose the new suppression method for breathing oscillations in the hall thrusters