Landscape Dynamics, Articles

Selected papers of Ralph Abraham

MS#68. North-South trade and the dynamics of the environment, 1994
with Graciela Chichilnisky and Ron Record. In: Sustainability: Dynamics and Uncertainty, G. Chichilnisky, G. M. Heal, and A. Vercelli, eds. Kluwer Academic Publishers, The Netherlands, 1998, pp. 77-108. [PDF], ca 3 MB
Abstract. We develop a discrete dynamical system for economic behavior of a North-South model of international trade. Capital stocks of the North and the South increase endogenously through time, defining an iterated dynamical system on the plane. Our simulations reveal the response diagram for this dynamic system with one of the coefficients of the model (a variable representing property rights on environmental resources) as control parameter. As property rights vary we establish the existence of oscillations, period doubling bifurcations, chaotic behavior, and multistability. We discuss the implications for business cycles, and the interaction of economic and environmental variables.
MS#98. Complex Dynamical Systems, 1998. Preprint, [PDF] 16 KB
Abstract. A concise introduction to the basic concepts of complex dynamical systems, in the context of the new mathematical theories of chaos and bifurcation.
MS#110. Neural Networks for Economic Prediction, 2003.
Preprint. With Lionello Punzo, [RTF] 16 KB

Revised 17 October 2004 by Ralph Abraham