This paper discusses the mathematical validity of the class of linear periodically time varying compartment models which are commonly employed for the analysis of ecosystems. Valid mathematical models for such systems must have unique stable periodic solutions to which all other solutions converge.
An environ analysis for nonlinear compartment models
β Scribed by T.G. Hallam; M.N. Antonios
- Publisher
- Springer
- Year
- 1985
- Tongue
- English
- Weight
- 566 KB
- Volume
- 47
- Category
- Article
- ISSN
- 1522-9602
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β¦ Synopsis
Environ analysis, an input-output analysis for models of ecological systems,'has been previously formulated for linear systems. This note has a twofold purpose: first, we indicate that a variation of parameters technique can be applied, at least in principle, to compute both input and output environs; and second, we show that this technique may be used for computation of environs in nonautonomous, nonlinear compartment models, This nonlinear theory, obtained as a direct extension of dynamical system developments, allows the traditional environ partitioning of compartmental storages and flows. An example of a nonlinear nutrient-producer-consumer system whose output environs can be computed asymptotically is presented to illustrate these concepts.
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