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The Studies on the Behavior of the Solutions to the Nonlinear Market Diffusion Models in Competition Environment

Author: XiongDeXian
Tutor: PanTao
School: Jinan University
Course: Basic mathematics
Keywords: Nonlinear Market Diffusion Competitive environment Cumulative sales Instantaneous sales Advertising intensity factor The total number of potential consumers
CLC: F274
Type: Master's thesis
Year: 2008
Downloads: 47
Quote: 0
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Abstract


Update diffusion process of the products in the market , is an important topic of market research , market forecasts and enterprises to develop reasonable price , advertising strategies have an important role . This article discusses two consumer durables market competition diffusion process to study the behavior of solutions of nonlinear market diffusion model . Bass model is based on the nonlinear market diffusion models to establish a competitive environment . Respectively in advertising intensity coefficient K and the total number of potential consumers Sectional variable circumstances , deduced accumulated sales function of N (t ) , the the instantaneous sales function P (t), sales mature initial time T_ * sales the peak moment t_m, sales period of recession initial time t ~ * analytical expression . Around T_ * T_m , t ~ * These decisions accumulated sales curve and instantaneous sales curve behavior of the characteristics of moments , demonstration under certain conditions , with the the advertising intensity coefficient a K of the total number of potential consumers increase their increment, decrement the case . On this basis , the the accumulated sales curve and instantaneous sales curve various forms , and its system of classification . Finally, the use of Microsoft Office Excel2003 statistical procedures as well as Adobe Photoshop software tools , given the theoretical results of numerical simulation .

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