Foreword to the special issue on nonlinear economic dynamics

Abstract

The theory of dynamical systems has been one of the most developed mathematical areas in the last 50years with a wide spectrum of applications ranging from physics to biology to economics. During the last decades, economic theory in particular has witnessed an important shift in methodology. The classical approach that describes economic outcomes as resulting from the choices of fully rational and identical economic agents has failed to explain many important features of economic complexity in the real world. Fueled by its inability to predict sudden changes and (financial and economic) crises, it has been criticized on a number of grounds. As a consequence, a growing interest in alternative approaches based on concepts like bounded rationality and heterogeneity, social interaction, and learning has emerged. Following this new paradigm, economics and finance are viewed as complex evolving systems characterized by emerging non-equilibrium situations. The corresponding mathematical modeling approaches require a wide range of analytical and numerical techniques, some of which are new and innovative. These techniques consist of a mix of theories, among them the qualitative theory of nonlinear dynamical systems, optimal control theory, game theory, and the theory of stochastic processes. The current status and the upcoming trends of these new modeling techniques and numerical toolswere presented at the InternationalConferenceonNonlinearEconomic