Dynamics of Technological Development: Innovation, Imitation, Depreciation

Abstract

The nonlinear dynamical system, describing the dynamics of sector capital distribution over two levels of technological development, low and high, proposed. The dynamics is determined by the interaction of innovation and imitation process with the process of depreciation taking into account. The qualitative behavior of the system trajectories depending on the relationship of parameters determining the rates of innovation, imitation and depreciation processes is studied. The invariant set which all trajectories enter in a finite time is found. In the case of nonzero rate of innovation process, the uniqueness of equilibrium is proved. On the basis of proposed constructive geometrical method the sufficient conditions of its global stability are obtained. In order to study the behavior of isoclines the special curve parametrization, connected with the invariant set geometry, is proposed. It is shown that in the absence of innovation process the existence of two equilibria, stable and unstable, is possible. In addition, the transition to a high technological level, corresponding to a stable equilibrium, may not occur even under sufficiently small depreciation process rate. The bifurcation value of the imitation rate parameter is found.