TY - JOUR

T1 - Aggregation in model ecosystems II. Approximate aggregation

AU - Iwasa, Yoh

AU - Levin, Simon A.

AU - Andreasen, Viggo

PY - 1989/12/1

Y1 - 1989/12/1

N2 - 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.

AB - 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.

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U2 - 10.1093/imammb/6.1.1-a

DO - 10.1093/imammb/6.1.1-a

M3 - Article

AN - SCOPUS:0001770062

VL - 6

SP - 1

EP - 23

JO - Mathematical Medicine and Biology

JF - Mathematical Medicine and Biology

SN - 1477-8599

IS - 1

ER -