Evolutionary models of innovation dynamics

We investigate the dynamics of social processes and, in particular, processes of innovation in socio-economical evolution, technological change, and scientific research in discrete and continuous state spaces. The discrete description is based on the occupation number formalism and transition probabilities (Master equation formalism). Our special attention is devoted to the creation and survival of the NEW (i.e., new behavior, new technologies, new ideas etc.). The second (continuous) model is based on the idea that evolution is hill-climbing in an adaptive landscape over a continuous characteristics space. The behavior of an individual, a technological product, or a scientific problem is described by a large number of characteristics covering behavioral aspects, technology-inherent and economic parameters, or thematic dimensions. Further, we define a real-valued multi-modal fitness function/functional and a population density over the characteristics space. The evolutionary dynamics including competition and innovations is modeled by reaction-diffusion equations of Fisher-Eigen or Lotka-Volterra type.