Stochastic dynamics of instabilities in evolutionary systems

This article develops a modeling framework that allows a formal description of evolutionary processes in social and biological systems. An enumerable set of fields (chemical sorts, biological species, technologies, areas of scientific endeavor, and so on) is considered, each field being characterized by the number and properties of its representatives (occupying elements). By introducing probabilities for the elementary processes of spontaneous generation, identical self-reproduction. error reproduction, death. and transition to other fields, we define a Markov process in occupation number space. At any time, only a finite set of fields is occupied, and the appearance of a representative of a field with "better" properties produces an instability in the system. The characteristic dynamics of such "innovative instabilities" are investigated by simulation. As a particular example, we consider the nonlinear growth properties associated with the emergence of new areas of scientific research.