Ecological and Lyapunov Stability
Justus, James (2006) Ecological and Lyapunov Stability. In [2006] Philosophy of Science Assoc. 20th Biennial Mtg (Vancouver): PSA 2006 Contributed Papers.
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Abstract
Ecologists have proposed several incompatible definitions of ecological stability. Emulating physicists, mathematical ecologists commonly define it as Lyapunov stability. This formalizes the problematic concept by integrating it into a well-developed mathematical theory. The formalization also seems to capture the intuition that ecological stability depends on how ecological systems respond to perturbation. Despite these advantages, this definition is flawed. Although Lyapunov stability adequately characterizes perturbation responses of systems typically studied in physics, it does not for ecological systems. This failure reveals a limitation of its underlying mathematical theory, and an important difference between dynamic systems modeling in physics and biology.
| Keywords: | stability, ecology, Lyapunov, Liapunov, definition, perturbation, dynamic systems modeling |
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| Subjects: | General Issues: Models and Idealization Specific Sciences: Mathematics Specific Sciences: Biology: Ecology/Conservation |
| Conferences and Volumes: | [2006] Philosophy of Science Assoc. 20th Biennial Mtg (Vancouver): PSA 2006 Contributed Papers |
| ID Code: | 2987 |
| Deposited By: | Justus, James |
| Deposited On: | 16 October 2006 |