Where Can One Hope to Profitably Apply the Ideas of Chaos?

JUL 01, 1994

A number of theoretical and practical issues must be considered when attempting to carry out meaningful analyses of real systems such as planetary orbits, heartbeats and economics in terms of chaos theory.

DOI: 10.1063/1.881395

David Ruelle

The success of the ideas of chaos has led to attempts to apply them to a great variety of situations. This is in principle a good strategy, but the results are not always up to expectations. In some cases the results are predictably of little interest. Suppose you have concocted a mathematical model in biology or economics; you put this model on your computer and you discover a Feigenbaum period‐doubling cascade, which is often a sign that chaos is present. Is this result interesting? Well, probably not. One reason is that the detailed dynamical properties of your model may not have anything to do with the properties of the real‐life system. Another reason why your discovery may be without interest is that the occurrence of a Feigenbaum cascade need not have any particular biological or economic significance: You still have to address the problem of the relevance of your finding for biology or economics.

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More about the Authors

David Ruelle. Institut des Hautes Etudes Scientifiques, Bures‐sur‐Yvette, France.