A dynamical systems approach to energy balance models of climate is presented, focusing on low order, or conceptual, models. Included are global average and latitude-dependent, surface temperature models. The development and analysis of the differential equations and corresponding bifurcation diagrams provides a host of appropriate material for undergraduates.
Jim Walsh (firstname.lastname@example.org) specializes in dynamical systems, having earned a Ph.D. from Boston University under the direction of G.R. Hall in 1991. His research interests increasingly center on applied dynamical systems and mathematical modeling. He is fortunate to have had the opportunity to spend a recent sabbatical at the University of Minnesota, participating in Richard McGehee’s seminar on mathematics and climate. He is, above all, lucky to be the husband of Debbi and father of Zachary and Alexandra.
Richard McGehee (email@example.com) received a Ph.D. from the University of Wisconsin in 1969. Following a post-doctoral appointment at the Courant Institute of Mathematical Sciences, he joined the University of Minnesota faculty in 1970, where he has been ever since. He has held visiting positions at the ETH in Zurich, Switzerland, and at IMPA in Rio de Janiero, Brazil. He was also the Visiting Ulam Professor at the University of Colorado at Boulder. He is a founding member of the Mathematics and Climate Research Network (MCRN) and runs a research seminar on the mathematics of climate, which has been meeting weekly since 2007 and which is broadcast over the internet to participants throughout the country. His current research involves studying conceptual climate models as dynamical systems and comparing their behavior to the climate record.