William Brock

In Search of the Elusive Early Warning Signal of Tipping Points, Critical Transitions, and Abrupt Regime Changes in Ecology and Economics: A Report From the Front

April 14, 2011

William Brock is Vilas Research Professor at the University of Wisconsin—Madison. He earned a doctorate in mathematics from the University of California, Berkeley in 1969. He has served on the faculties of the University of Rochester, the University of Chicago, Cornell University and the University of Wisconsin—Madison. His dissertation and early work were on optimal growth theory. His proof of the existence of a growth program that is maximal with respect to the catching-up criterion was an especially notable contribution.

Other important contributions were his proofs of the turnpike theorem and of the existence of a stationary program for a single sector stochastic growth model. This work was followed by a large number of significant papers on the stability of stochastic growth paths and of optimal control systems. In the late 1970s, Brock and collaborators modeled the determination of tariffs in a democratic country as the outcome of a dynamic game among politicians, interest group lobbyists and the electorate.

In the 1980s Brock developed an interest in chaotic deterministic systems and their application to economics and finance. He made major contributions to the development of statistical tests for the presence of a chaotic deterministic process for generating a time series. Since the late 1990s, he has applied optimal control theory to environmental management issues.