In this article, an innovation diffusion model with the nonlinear acceptance is proposed to describe the dynamics of three competing products in a market. It is proved that the model admits a unique positive equilibri...In this article, an innovation diffusion model with the nonlinear acceptance is proposed to describe the dynamics of three competing products in a market. It is proved that the model admits a unique positive equilibrium, which is globally stable by excluding the existence of periodic solutions and by using the theory of three dimensional competition systems.展开更多
In this article, a nonlinear mathematical model for innovation diffusion with stage structure which incorporates the evaluation stage （time delay） is proposed. The model is analyzed by considering the effects of ext...In this article, a nonlinear mathematical model for innovation diffusion with stage structure which incorporates the evaluation stage （time delay） is proposed. The model is analyzed by considering the effects of external as well as internal influences and other demographic processes such as emigration, intrinsic growth rate, death rate, etc. The asymptotical stability of the various equilibria is investigated. By analyzing the exponential characteristic equation with delay-dependent coefficients obtained through the variational matrix, it is found that Hopf bifurcation occurs when the evaluation period （time delay, T） passes through a critical value. Applying the normal form theory and the center manifold argument, we de- rive the explicit formulas determining the properties of the bifurcating periodic solutions. To illustrate our theoretical analysis, some numerical simulations are also included.展开更多
The innovations actually diffuse among social network nowadays.Individual heterogeneity,interactions between individuals and network topology influence a lot.We established a "double threshold" modified mode...The innovations actually diffuse among social network nowadays.Individual heterogeneity,interactions between individuals and network topology influence a lot.We established a "double threshold" modified model and took the number of neighbors,neighbors' adoption and the cost-benefit parameters as crucial influencing factors.The diffusion of DaLingTong(CDMA450)products in MeiShan city of SiChuan province during 2004 to 2007 has been used to verity the model on Matlab.The validation results fit the actual diffusion pattern of DaLingTong(CDMA450) products very well.The results indicate that there exists a "tipping point(threshold)" in the process of innovation diffusion.If the initial adoption quantity is larger than the tipping point,then the product will spread to a large portion of people,otherwise is will collapse to zero.The model can effectively predict the diffusion of new products,and can influence the diffusion process by changing the value of the parameters.展开更多
基金Project Supported by the National Natural Science Fund of China(10571143) the Research Fund of Southwest Normal University
文摘In this article, an innovation diffusion model with the nonlinear acceptance is proposed to describe the dynamics of three competing products in a market. It is proved that the model admits a unique positive equilibrium, which is globally stable by excluding the existence of periodic solutions and by using the theory of three dimensional competition systems.
基金the Support Provided by the I.K.G. Punjab Technical University,Kapurthala,Punjab,India,where one of us(RK) is a Research Scholar
文摘In this article, a nonlinear mathematical model for innovation diffusion with stage structure which incorporates the evaluation stage （time delay） is proposed. The model is analyzed by considering the effects of external as well as internal influences and other demographic processes such as emigration, intrinsic growth rate, death rate, etc. The asymptotical stability of the various equilibria is investigated. By analyzing the exponential characteristic equation with delay-dependent coefficients obtained through the variational matrix, it is found that Hopf bifurcation occurs when the evaluation period （time delay, T） passes through a critical value. Applying the normal form theory and the center manifold argument, we de- rive the explicit formulas determining the properties of the bifurcating periodic solutions. To illustrate our theoretical analysis, some numerical simulations are also included.
基金ACKNOWLEDGEMENTS Project supported by the National Social Science Foundation of China （Grant No. 11BGL041）, Ministry of Education Humanities and Social Sciences General Project （12YJA630166）.
文摘The innovations actually diffuse among social network nowadays.Individual heterogeneity,interactions between individuals and network topology influence a lot.We established a "double threshold" modified model and took the number of neighbors,neighbors' adoption and the cost-benefit parameters as crucial influencing factors.The diffusion of DaLingTong(CDMA450)products in MeiShan city of SiChuan province during 2004 to 2007 has been used to verity the model on Matlab.The validation results fit the actual diffusion pattern of DaLingTong(CDMA450) products very well.The results indicate that there exists a "tipping point(threshold)" in the process of innovation diffusion.If the initial adoption quantity is larger than the tipping point,then the product will spread to a large portion of people,otherwise is will collapse to zero.The model can effectively predict the diffusion of new products,and can influence the diffusion process by changing the value of the parameters.
