The Studies On The Behavior Of The Solutions To The Nonlinear Market Diffusion Models In Competition Environment

The diffusion process of product in the market is an important problem of market research.Because it has an important role in forecasting market,development of prices, choosing reasonable advertising strategy and so on.In this paper,the behavior of the solutions of the non-linear market diffusion models,which describes the market competition diffusion process of two consumer durable,was studied.Based on the Bass model,the non-linear market diffusion models in competition environment was established.In the case of advertising intensity factor a that is sub-variable or the total number of potential consumers K that is sub-variable,the analytical expression of cumulative sales function N(t),instantaneous sales function P(t).the initial point of sales maturity period t_*,the peak time of sales period t_m,the initial point of sales recession period t~* were deducted respectively.Surrounding these characteristic times t_*,t_m,t~*,which determine the behavior of cumulative sales curve and instantaneous sales curve,the states of the incrementing or decrementing of 3 characteristic times asα,K increasing gradually was proved under certain conditions,respectively.On this basis,various types of cumulative sales curve and instantaneous sales curve were analyzed and classified.Finally.the numerical simulations of the theoretical results were given by using statistical procedures of Microsoft Office Excel2003 and image processing software of Adobe Photoshop.