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
Strategic innovation diffusion converts newly created knowledge into increasing a firm’s value primarily through innovative product offerings.In this paper,we present a time-based adoption pattern with pricing and pr...Strategic innovation diffusion converts newly created knowledge into increasing a firm’s value primarily through innovative product offerings.In this paper,we present a time-based adoption pattern with pricing and promotional expenditure as a three-dimensional innovation diffusion model(3D-IDM).In our proposed 3D-IDM,we assume that value of the product plays a crucial role of being the major driver of diffusion,and is classified into the following three main factors:(1)continuation time of the product in the market–representing goodwill of the product;(2)price of the product–indicating consumers’buying behaviour;and(3)marketing efforts of the firm.A special form of the Cobb–Douglas production function is used to design the three-dimensional framework.An empirical study is performed on number of consumer-durable sales data to validate and compare the proposed model.Various performance measures are treated uniquely using the Mahalanobis distance-based approach(DBA)to determine the relative strength of each model.展开更多
In this paper, the model of competing technologies diffusion was set up in order to analyze the relationship of competing technologies in diffusion process, and the stability of diffusion model with two kinds of compe...In this paper, the model of competing technologies diffusion was set up in order to analyze the relationship of competing technologies in diffusion process, and the stability of diffusion model with two kinds of competing technologies was analyzed. It is concluded that dominator can hold competing vantage by suppressing its opponent, and besides, whether competing technology can gain superiority in diffusion process depends on the success rates of technology diffusion when the two kinds of technology match each other in strength.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.
文摘Strategic innovation diffusion converts newly created knowledge into increasing a firm’s value primarily through innovative product offerings.In this paper,we present a time-based adoption pattern with pricing and promotional expenditure as a three-dimensional innovation diffusion model(3D-IDM).In our proposed 3D-IDM,we assume that value of the product plays a crucial role of being the major driver of diffusion,and is classified into the following three main factors:(1)continuation time of the product in the market–representing goodwill of the product;(2)price of the product–indicating consumers’buying behaviour;and(3)marketing efforts of the firm.A special form of the Cobb–Douglas production function is used to design the three-dimensional framework.An empirical study is performed on number of consumer-durable sales data to validate and compare the proposed model.Various performance measures are treated uniquely using the Mahalanobis distance-based approach(DBA)to determine the relative strength of each model.
文摘In this paper, the model of competing technologies diffusion was set up in order to analyze the relationship of competing technologies in diffusion process, and the stability of diffusion model with two kinds of competing technologies was analyzed. It is concluded that dominator can hold competing vantage by suppressing its opponent, and besides, whether competing technology can gain superiority in diffusion process depends on the success rates of technology diffusion when the two kinds of technology match each other in strength.
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.
