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Searching Explanations of Nature in the Mirror World of Math

Marten Scheffer, Wageningen Agricultural University

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Abstract

Despite the huge scientific progress of the last century, the dynamics of complex systems such as the atmosphere, human societies, and ecosystems remain difficult to understand and predict. Nonetheless, our ability to carve the future depends largely on our insight into the functioning of such complex systems. Complex systems are the focus of considerable mathematical theory. Rather than referring to any particular part of the world, such theory addresses what seems to be another world: a world of strange attractors, catastrophe folds, torus destruction, and homoclinic bifurcations. So disparate is the language and notation in this discipline that it is hard to imagine that it has any thing to do with reality as we know it. Indeed, it deals with a kind of mirror world, but in fact, underlying structures of the real world show up in this mirror world with a beautiful clarity that can never be seen in reality. This essay is about the relationship between this world and reality. Examples are taken from the work on aquatic ecosystems, starting with a view on the scale of entire lakes that can have multiple stable states, then zooming in on food web interactions in the lake, and further down to reveal chaos in the algal community.

Key words

bifurcation, catastrophe, chaos, cycle, Daphnia, fish, macrophyte, model, multiple stable states, plankton, predation, trophic cascade
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Ecology and Society. ISSN: 1708-3087