Product Sales Network In The Dynamics Modeling And Analysis

The rapid development of Internet makes people face a large amount of information, i.e.information overload. As a result, it’s so hard to find the required information from the te-dious information. Therefore, we need to filter information by using some common methodssuch as search engines, which needs to input some keywords in address bar to get the relativewebpages. However, using the search engine to filter information has some shortcomings anduntil now, the most efective way to filter information is to provide personalized recommen-dation, which based on the users’ interests and purchasing behavior to recommend usersthe interested information and products. Generally, a complete recommendation system iscomposed of three parts: collecting users’ behavior mode, analyzing users’ favorites modelmode and recommendation algorithm mode. And the recommendation algorithm mode isthe central part. Up to now, the recommendation algorithm mainly include collaborativefiltering, content-based analysis, user-product bipartite graph-based analysis, hybrid recom-mendation algorithm and so on. Nevertheless, the research on the current recommendationalgorithm of personalized recommendation system combining certain background to analyzeuser-product dynamics is a bit little. So this paper makes the following researches:1.According to the user-product bipartite graph, the recommendation algorithm has arelative recommendation internet and through this user-product bipartite graph, this papermainly studies the changes in the number of users who used diferent brand of product.The major considering product is fast moving consumer goods and the considering users arecommon groups. The three characteristics of fast moving consumer goods are convenience,visualization, low brand loyalty, determine that the habit of users to purchase these productsis just easy, fast, impulsive and sensitive. According to the background, this article estab-lishes a n+1dimensional dynamical model which describes the changes of the number of usersusing diferent brand products. When the way users choosing one certain brand product israndom attachment or preference attachment, the paper performs numerical simulation anddynamic analysis, then obtains that the system would tend to stable. 2. When the choosing way is random attachment, the model is numerical simulated.Also, And in particular simple cases which set the number of users is2, and at each time’sstep, there is only one user who hasn’t chosen the certain product can choose the product, themodel theoretically was analyzed, the only equilibrium E0could be obtained and the localasymptotic stability could also be proved by utilizing Jacobian matrix. Through constructingDulac function, no closed orbit could be proved, then the global asymptotic stability of theequilibrium could be got, and after that, using numerical simulation to check the conclusion.3.When the choosing way is preference attachment, the dynamical model is establishedwhich describes the changes of number of users to choose diferent brand products, the onlyequilibrium E1could be obtained and the local asymptotic stability of the equilibrium E1could also be proved by constructing Lyapunov function, and the numerical simulation ofthis model is also performed. And in the same specific simple cases, the model theoreticallywas analyzed, the only equilibrium E2could be obtained. Through constructing Lyapunovfunction, the global asymptotic stability of the equilibrium E2could be got, and after that,using numerical simulation to check the obtained conclusion. Finally,we can get that whenattached randomly, one certain product would not appear brand monopoly and each brandproduct would develop with benign competition. As a consequence, every brand productswould develop at balance. But when attached preferentially, at first, the more degree thebrand has, the more percentage the brand would have. While after long time, the old brandproducts would be replaced by the new ones till the old ones die out.