• International Journal of Technology (IJTech)
  • Vol 11, No 6 (2020)

Three-Dimensional Trends Superposition in Digital Innovation Life Cycle Model

Three-Dimensional Trends Superposition in Digital Innovation Life Cycle Model

Title: Three-Dimensional Trends Superposition in Digital Innovation Life Cycle Model
Vladimir F. Minakov, Oleg S. Lobanov, Sergey A. Dyatlov

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Cite this article as:
Minakov, V.F., Lobanov, O.S., Dyatlov, S.A. 2020. Three-Dimensional Trends Superposition in Digital Innovation Life Cycle Model. International Journal of Technology. Volume 11(6), pp. 1201-1212

Vladimir F. Minakov St. Petersburg State University of Economics, 21, Sadovaya Street, 191023 St. Petersburg, Russian Federation
Oleg S. Lobanov St. Petersburg State University of Economics, 21, Sadovaya Street, 191023 St. Petersburg, Russian Federation
Sergey A. Dyatlov St. Petersburg State University of Economics, 21, Sadovaya Street, 191023 St. Petersburg, Russian Federation
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Three-Dimensional Trends Superposition in Digital Innovation Life Cycle Model

The concept of innovative products’ life cycle as a superposition of growing interest in their consumption, as well as processes of falling demand, is substantiated in this study. This study found that such trends in the life cycle of innovations are unified. The development of the economic and mathematical model is based on the method of these trends’ superposition. The result of this superposition is the unity of the mathematical representation of simultaneously occurring processes in the rise in demand for innovative products, consumer disappointment or crowding out by competitive innovative solutions. The mathematical description of each process is an original mathematical form that reflects the diffusion phenomena, which differs in the expression of the mathematical model parameters in the indicators form of real-time series of innovative products consumption. The principle of superposition and the unity of trends in the growth and decline of consumer interest in innovative products makes it possible to proactively establish the formation towards changing trends in the dynamics of innovative product consumption. These distinctive features of the model ensure transition from a qualitative to a quantitative representation of the Gartner cycle. This allows the use of the developed model to solve the problems of forecasting the consumption of innovations. In the growth phase, the processes of transition to the plateau of innovation success, the reversal of the growth trend and the onset of recession were identified. In the phase of movement to recession of the hype, the model makes it possible to predict the time of transition to an increase in consumption and to a plateau of innovation success. A special case of the proposed model is the cycle curve developed by Gartner in a descriptive form. The mathematical representation of such a case expands the applicability of the model to quantitative indicators of innovation processes.

Change management; Cycles; Digital economy; Economic and mathematical model; Innovation management


The manifestation of these processes is especially noticeable in the automotive market (Borisov and Pochukaeva, 2019) (suffice it to recall the filing of a bankruptcy petition for the world capital of the automotive industry of Detroit in 2013). In addition, there are problems of effective management of innovation and investment processes (Sklyarova et al., 2019). The changeable stages of success and problems in Elon Musk's companies are indicative.

Consequently, there is a need for the evolution of modeling methods in innovation management (Minakov et al., 2017; Glinskiy et al., 2018b). Indeed, Rogers' models and similar ones (Rogers, 2004; Rogers, 2015) reflected only the main processes and phases of the life cycle (the spread of innovations among “innovators, early adopters, early majority, late majority, lagging behind”). The lack of such models led to the formalization of local processes (including short-term) declines in interest in innovation (Rivera et al., 2006), followed by a partial or complete restoration of their spread (1995, model of hype cycles proposed by Gartner).

It is also important to note that the role of innovation has grown significantly in connection with the digitalization of the economy (Barykin et al., 2020). First, solutions in the field of information technology (IT solutions) have gone beyond the framework of auxiliary tools used by the personnel of enterprises to improve the efficiency of their activities (Karlik et al., 2019). They have long and successfully performed the functions of automation and control systems. ERP systems have expanded the boundaries of the use of information and communication systems and technologies (ICT) to business processes that go beyond enterprises – manufacturers of goods and services (Silkina et al., 2019). A large cluster of smart solutions has separated employees from functional processes implemented by automated IT solutions with elements of artificial intelligence. In addition, intelligent systems and technologies have put individuals in a position of dependence on capabilities and, for example, “smart proposals” of information systems based on intellectual analysis of data on the needs and preferences of a person based on his digital prints and traces (Ignatiev et al., 2019; Karlik et al., 2020).

Digital resources have played a significant role in the global economy during the COVID-19 pandemic. They have shown substitute properties in relation to traditional production factors. The most ambitious innovative role of ICT manifested itself as infrastructure (Dyatlov et al., 2018; Glinskiy et al., 2020), when its previous form did not meet the requirements of limiting physical interaction in the population to prevent the spread of coronavirus.

At the same time, to date, no economic and mathematical model has been created for detailing the life cycle of digital innovations, which would include a cycle of excitement. In this regard, the scientific task of verifying such a model is relevant. Based on this, the aim of this study is to develop economic and mathematical models of the innovation diffusion dynamics by phases of declining demand. In this regard, tasks of analyzing economic and mathematical models of innovative changes life cycle that have been completed to date should be solved, as well as the development of an approach to verify such models in the phase of decline in the innovation diffusion rate.


The concept of innovation processes represented as a superposition of diffusion trends made it possible to verify the economic and mathematical models of innovation diffusion, which is distinguished through an adequate mathematical description of the complete life cycle of innovation. In this case, a special model is the model of agiotage cycles proposed by Gartner. In this model, manifestation and diffusion result in the processes of rush demand. An increase in consumption due to an increased consumer value of innovative products compared to existing and traditional products and a decrease in demand due to the formation of opposing factors. These opposing factors include a lack of financial resources and an avalanche effect on the company, which includes manufacturing of innovative products, risks arising from the use of innovation by consumers (for example, information, in information and communication systems), the influence of competitive environment, the development of alternative innovative solutions and many others. In the economic and mathematical model developed, the superposition of growth and decline processes in the consumption of innovative products not only increases the accuracy of modelling innovative processes but also obtains new predictive indicators (leading indicators). Therefore, by identifying the parameters of this model, the presence or absence of a decline trend and, consequently, the subsequent breakdown of the general trend in innovative products sales dynamics are identified. The authors carried out modelling and obtained quantitative results for the rush cycle of innovations spread for the following parameters: to = 200; t_ = 233; k=0.7; T = 44; Tn = 11. In addition, a calculation was performed and a three-dimensional representation of demand indicators for innovative products was obtained when the ratio of the growth parameters of demand diffusion and its inhibition (k in the range from 0.1 to 0.8) were changed. The results obtained (demand level V) in three-dimensional representation are the basis of managerial decisions in innovation management systems, which include activating advertising, increasing production volumes, attracting and distributing financial, labor and other resources (or vice versa) and modernizing or disposing outgoing innovative solutions. Thus, the developed model, as well as new indicators of innovation processes obtained on its basis, will increase the efficiency of digital innovation management invariant to the type of digital innovative product.


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