Studies On The Behavior Of The Solutions To The Non-linear Market Diffusion Models

In this paper,the behavior of the solutions to the non-linear market diffusion model was studied.Based on the Bass model,the behavior of the solutions were discussed in the cases of diffusion coefficient a that is sub-variable,diffusion coefficient b that is subvariable and the total number of potential consumers K that is sub-variable,respectively.In the cases of diffusion coefficient a that is sub-variable,diffusion coefficient b that is sub-variable and the total number of potential consumers K that is sub-variable,the analytical expressions of cumulative sales volume function N(t),sales function P(t),the initial point of the market mature period t.,the peak time of market period t_M,the initial point of the market recession period t^* and the maximal sales volume P_max was derived, respectively.The states of the incrementing or decrementing of 3 characteristic times t_*, t_M,t^* as a,b,K increasing gradually were proved under certain conditions,respectively. On this basis,analyzed the various types of cumulative sales volume function N(t),sales function P(t),and given clear classification.Finally,the numerical simulations of the theoretical results were given by using statistical procedures of Microsoft Office Excel and Photoshop image processing software.