Singularity bifurcations

Abstract

Abstract:Euler equation models represent an important class of macroeconomic systems. Our ongoing research (He and Barnett (2003)) on the Leeper and Sims (1994) Euler equations macroeconometric model is revealing the existence of singularity-induced bifurcations, when the model's parameters are within a confidence region about the parameter estimates. Although known to engineers, singularity bifurcation has not previously been seen in the economics literature. Knowledge of the nature of singularity-induced bifurcations is likely to become important in understanding the dynamics of modern macroeconometric models. This paper explains singularityinduced bifurcation, its nature, and its identification and contrasts this class of bifurcations with the more common forms of bifurcation we have previously encountered within the parameter space of the Bergstrom and Wymer (1976) continuous time macroeconometric model of the UK economy.

Acoustic predation in a sailfish-flying fish cloak

“…There is evidence that the sailfish motion then is opposite to the school 1 . The instability is modeled as a one dimensional pitchfork instability given by 33 . The steady state solutions for and are shown in Fig.…”

From Sunspots to Black Holes: Singular Dynamics in Macroeconomic Models

“…in the study of Black holes), economists have tended to look the other way. There are a few exceptions: Barnett and He (2010) and He and Barnett (2006) are, to our knowledge, the only papers dealing with the importance of singularities in economic models (in their case associated to the introduction of feedback policy rules). Singularities play a large role in other scientific fields and we believe that we also need to understand their potential role in macroeconomic dynamics.…”