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Multiple Stable States in Natural Ecosystems$
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Peter Petraitis

Print publication date: 2013

Print ISBN-13: 9780199569342

Published to Oxford Scholarship Online: May 2015

DOI: 10.1093/acprof:osobl/9780199569342.001.0001

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What theory actually tells us about multiple stable states

What theory actually tells us about multiple stable states

Chapter:
(p.10) (p.11) 2 What theory actually tells us about multiple stable states
Source:
Multiple Stable States in Natural Ecosystems
Author(s):

Peter Petraitis

Publisher:
Oxford University Press
DOI:10.1093/acprof:osobl/9780199569342.003.0002

This chapter examines the differential equations used for the modeling of ecological process of multiple stable states. The equations quickly reveal what experimentalists can test; thus, the discussion of theory in this chapter is limited to one-, two-, and three-species models of differential equations. Furthermore, the Allee or dispensation effects and multiple stable states for a single species is discuss to support the theory. In conclusion, this chapter argues that the complexity of the basins of attraction increases with the number of multiple stable states. In systems with two alternative states, the boundaries between two basins are smooth. However, as the number of stable states increase, the majority of the basins will have fractal boundaries.

Keywords:   differential equation, multiple stable state, theory, model, Allee effect, dispensation effect

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