This paper is an up-to-date survey of the state of the art in dynamical systems theory relevant to high levels of dynamical complexity, characterizing chaos and near-chaos, as commonly found in the physical sciences. The paper also surveys applications in economics and finance. This survey does not include bifurcation analyses at lower levels of dynamical complexity, such as Hopf and transcritical bifurcations, which arise closer to the stable region of the parameter space. We discuss the geometric approach (based on the theory of differential/difference equations) to dynamical systems and make the basic notions of complexity, chaos, and other related concepts precise, having in mind their (actual or potential) applications to economically motivated questions. We also introduce specific applications in microeconomics, macroeconomics, and finance and discuss the policy relevance of chaos.

In the aftermath of the global financial crisis, questions have been raised regarding the value and applicability of modern macroeconomics. Motivated by these developments and recent advances in dynamical systems theory, the papers in this special issue of Macroeconomic Dynamics deal with specific aspects of the economy as a complex evolving dynamic system.

This paper presents a computable general equilibrium model of endogenous (stochastic) growth and cycles that can account for two key features of the aggregate data: balanced growth in the long run and business cycles in the short run. The model is built on Schumpeter's idea that economic development is the consequence of the periodic arrival of innovations. There is growth because each subsequent innovation leads to a permanent improvement in the production technology. Cycles arise because innovations trigger a reallocation of resources between production and R&D. The quantitative implications of the calibrated version of our model are very similar to those of Kydland and Prescott's (1982) model. Moreover, under some parameterizations, our model can correct two shortcomings of RBC models: It can account for the persistence in output growth and the asymmetry of growth within the business cycle.