Aggregation in model ecosystems II. Approximate aggregation

Yoh Iwasa, Simon A. Levin, Viggo Andreasen

Research output: Contribution to journalArticle

116 Citations (Scopus)

Abstract

In this paper, the authors study the problem of finding the best approximate aggregation of dynamical systems, by considering the dynamics for macrovariables such that a certain criterion of inconsistency between the aggregated and original systems is minimized. First, the aggregation giving the least square deviation of the vector fields is obtained for any nonlinear dynamical system. Second, the best aggregation of linear systems around equilibria is examined by minimization of various criteria, such as (1) the difference in vector fields, (2) the difference in variables at a certain time point, (3) the difference in temporally averaged variables, and (4) the temporal average of square difference in variables. Finally, the determination of parameters in nonlinear dynamical systems by sequential application of several optimality criteria is discussed. In short, the best aggregated system greatly depends on the choice of criterion, especially with regard to the selection of the time horizon and of the weighting for the initial state.

Original languageEnglish
Pages (from-to)1-23
Number of pages23
JournalMathematical Medicine and Biology
Volume6
Issue number1
DOIs
Publication statusPublished - Dec 1 1989

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Ecosystem
Ecosystems
Aggregation
Nonlinear dynamical systems
Agglomeration
ecosystem
Nonlinear Dynamical Systems
Vector Field
Least-Squares Analysis
Linear systems
Optimality Criteria
Dynamical systems
Inconsistency
Model
Weighting
Least Squares
Horizon
Deviation
Dynamical system
Linear Systems

All Science Journal Classification (ASJC) codes

  • Neuroscience(all)
  • Modelling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Environmental Science(all)
  • Pharmacology
  • Applied Mathematics

Cite this

Aggregation in model ecosystems II. Approximate aggregation. / Iwasa, Yoh; Levin, Simon A.; Andreasen, Viggo.

In: Mathematical Medicine and Biology, Vol. 6, No. 1, 01.12.1989, p. 1-23.

Research output: Contribution to journalArticle

Iwasa, Yoh ; Levin, Simon A. ; Andreasen, Viggo. / Aggregation in model ecosystems II. Approximate aggregation. In: Mathematical Medicine and Biology. 1989 ; Vol. 6, No. 1. pp. 1-23.
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