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
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.
[PDF] 16 KB
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