Global Dynamics Analysis of Homogeneous New Products Diffusion Model
A mathematical model with stage structures is presented that incorporates the awareness stage and the decision-making stage; individuals exchange product information by two channels: mass media and interpersonal communication. When the persuasive advertisement is neglected in the decision-making sta...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2013/158901 |
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| _version_ | 1849406897713577984 |
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| author | Shuping Li Zhen Jin |
| author_facet | Shuping Li Zhen Jin |
| author_sort | Shuping Li |
| collection | DOAJ |
| description | A mathematical model with stage structures is presented that incorporates the
awareness stage and the decision-making stage; individuals exchange product information by two
channels: mass media and interpersonal communication. When the persuasive advertisement is
neglected in the decision-making stage, we find a threshold value about whether new products
diffusion is successful or not. When the persuasive advertisement is considered, there must exist a
positive equilibrium under some parameter condition; moreover, it must be globally asymptotically
stable as long as it exists. Results show that the persuasive advertisement in the decision-making
stage does not influence new products' successful diffusion, but the critical value that new products
diffuse successfully decreases when the persuasive advertisement is considered. Some numerical
simulations confirm our theoretical analysis and demonstrate the influence of parameters on the
system. Corresponding to the analysis results, some diffusion strategies are provided. |
| format | Article |
| id | doaj-art-4622a24af2fb49f3958d7e35835b7421 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-4622a24af2fb49f3958d7e35835b74212025-08-20T03:36:14ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2013-01-01201310.1155/2013/158901158901Global Dynamics Analysis of Homogeneous New Products Diffusion ModelShuping Li0Zhen Jin1School of Mechatronic Engineering, North University of China, Taiyuan 030051, ChinaDepartment of Mathematics, North University of China, Taiyuan 030051, ChinaA mathematical model with stage structures is presented that incorporates the awareness stage and the decision-making stage; individuals exchange product information by two channels: mass media and interpersonal communication. When the persuasive advertisement is neglected in the decision-making stage, we find a threshold value about whether new products diffusion is successful or not. When the persuasive advertisement is considered, there must exist a positive equilibrium under some parameter condition; moreover, it must be globally asymptotically stable as long as it exists. Results show that the persuasive advertisement in the decision-making stage does not influence new products' successful diffusion, but the critical value that new products diffuse successfully decreases when the persuasive advertisement is considered. Some numerical simulations confirm our theoretical analysis and demonstrate the influence of parameters on the system. Corresponding to the analysis results, some diffusion strategies are provided.http://dx.doi.org/10.1155/2013/158901 |
| spellingShingle | Shuping Li Zhen Jin Global Dynamics Analysis of Homogeneous New Products Diffusion Model Discrete Dynamics in Nature and Society |
| title | Global Dynamics Analysis of Homogeneous New Products Diffusion Model |
| title_full | Global Dynamics Analysis of Homogeneous New Products Diffusion Model |
| title_fullStr | Global Dynamics Analysis of Homogeneous New Products Diffusion Model |
| title_full_unstemmed | Global Dynamics Analysis of Homogeneous New Products Diffusion Model |
| title_short | Global Dynamics Analysis of Homogeneous New Products Diffusion Model |
| title_sort | global dynamics analysis of homogeneous new products diffusion model |
| url | http://dx.doi.org/10.1155/2013/158901 |
| work_keys_str_mv | AT shupingli globaldynamicsanalysisofhomogeneousnewproductsdiffusionmodel AT zhenjin globaldynamicsanalysisofhomogeneousnewproductsdiffusionmodel |