Modelling and analysis methods for economic characteristics variation in the innovation process have become a common technique, via employing diffusion equations for a medium with given parameters. The analysis results in this case significantly depend on the measurement accuracy of the industrial environment parameters, which is hard to achieve in practice. It seems, therefore, reasonable to make a transition from the diffusion paradigm to the innovation implementation paradigm, i.e., sequential modelling of the innovation states with variables and characteristics that correspond to the practical measurement and control techniques. Applying the described approach, the economic state dynamics of the innovation development work, manufacturing and implementation can be described by systems of ordinary differential equations, where the initial conditions and coefficients depend on the parameters of the industry’s internal andexternal environments. Two discrete mathematical models developed in this work enable control of the industrial environment parameters, via application of practical measurement methods. The first discrete model is in the form of a functional (mapping), which enables conversion of the actual internal industrial environment parameters in the beginning of the innovation scaling into the coefficients of the differential equations and initial conditions that reflect the results of manufacturing process preparation. The initial data is available from the EPR data base of the industry. The second discrete model is realized as a cellular automaton. An autonomous model of the external industrial environment uses the data that can be measured by the well-developed marketing methods. The results of the computational experiments support the hypothesis of transition from the diffusion model paradigm to the paradigm of the sequential modelling of the innovation economic states.
Белов В.Ф., Гаврюшин С.С., Маркова Ю.Н., Занкин А.И. Моделирование среды предприятия с использованием дискретных вычислительных алгоритмов.Математическое моделирование и численные методы, 2022, № 1, с. 109–128