Abstract: In this paper， we studied the solution of the discrete state of Malthusian model 〖SX（〗dx〖〗dt〖SX）〗=ax（1-x）, which is to determine the internal structure of the nonlinear first order difference equation xn+1=axn（1-xn）. According to different values of model parameter a， the model iteratively produce stable， nonstable （bifurcation） and chaotic results.