We formulate the model of growth scientific results in terms of dynamical system methods. First we review different approaches to dynamics ogf knowledge. Second we propose a new model of scientific development. It is assumed the existence of replacement of older papers by new more general results. For this aim we assume that the number of cited papers y represents the current knowledge stock. The second state variable is a number of all papers x. The rate of growth of cited papers depends on a constant which takes into account replaced old papers and the increase of new papers per a unit of the currentt knowledge stock. The dynamics of x is derived from the dynamical optimization procedure. In this nethod we maximize the functional of discounted increase of new results per a unit of current knowledge in an infinite time horizon. We investigate the hamiltonian system describing the evolution of the system on the phase plane (x,y). As a result we obtain that in the stationary state both variables grow with constant rates. We show that the critical point is a saddle point type and the optimized solution is unique and is represented by a separatrix approching this point. We demonstrate that at the final state all scientific results grow exponentially following the De Sola Price law.

• Legal notice:
  

  Copyright (c) Pielaszek Research, all rights reserved.
  The above materials, including auxiliary resources, are subject to Publisher's copyright and the Author(s) intellectual rights. Without limiting Author(s) rights under respective Copyright Transfer Agreement, no part of the above documents may be reproduced without the express written permission of Pielaszek Research, the Publisher. Express permission from the Author(s) is required to use the above materials for academic purposes, such as lectures or scientific presentations.
  In every case, proper references including Author(s) name(s) and URL of this webpage: https://science24.com/paper/12826 must be provided.

1. Methods of dynamical systems theory in modelling economic growth
2. The development of science as the factor of economic growth