The mathematical model of productivity- and age-structured scientific community evolution

Abstract

The productivity factor is very important at the mathematical simulation of scientific community evolution. In Ref. 1 the productivity index has been incorporated into the model exogenously to formulate the criterion of dynamic optimization of the scientific community age structure. In this paper we are going to include the productivity (as well as the age) in the individual state space and to derive the main dynamic equation which takes into account the stochastic fluctuations of scientific community members' productivity and some modifications of the Fokker-Planck equation. An approximation method for the evolution model is suggested with the aid of which the computational experiment is carried out. The discussion of experimental results and possible ways for improvement and extension of model are presented.

Knowledge Epidemics and Population Dynamics Models for Describing Idea Diffusion

“…(2) The master equation as a model of scientific productivity The productivity factor is a very important ingredient in mathematically simulating a scientific community evolution. One way to model such an evolution is through a dynamic equation which takes into account the stochastic fluctuations of scientific community members productivity [127] (Fig. 20).…”

“…The scientific community dynamics is described by a number density function n(a, ξ, t), -another form of scientific landscape, which specifies the age and productivity structure of the scientific community at time t. For example, the number of individuals with age in [a 1 , a 2 ] and scientific productivity in [ξ 1 , ξ 2 ] at time t is given by the integral a 2 a 1 ξ 2 ξ 1 da dξ n(a, ξ, t). A master equation for this function n(a, ξ, t) can be derived [127]:…”

“…Eq. ( 47) can be solved numerically or can be reduced to a system of ordinary differential equations [127].…”