TY - JOUR
T1 - Aggregation in model ecosystems II. Approximate aggregation
AU - Iwasa, Yoh
AU - Levin, Simon Asher
AU - Andreasen, Viggo
N1 - Funding Information:
Acknowledgements S.A.L. acknowledges National Science Foundation grants DMS-8406472 and BSR-8806202, and US Environmental Protection Agency Cooperative Agreement CR812685 with Cornell University. This research was supported in part by the Grant-in-Aid by the Ministry of Education, Science, and Culture of Japan, to Y.I. The final step of the work was done when both S.A.L. and Y.I. were in Oxford in 1988. We thank the Department of Zoology and the British Council (Y.I.) and the Centre for Mathematical Biology and All Souls' College of Oxford (S.A.L.) for their support. This is Report No. ERC-181 of the Ecosystems Research Center at Cornell University. The opinions expressed in the paper are those of the authors and do not necessarily represent those of the sponsoring agencies. We thank Joel E. Cohen, Don DeAngelis, Michael Gilpin, Alan Hastings, Hironori Hirata, Hirotsugu Matsuda, Hiroyuki Matsuda, Hans Metz, Takashi Miyata, Hisao Nakajima, Stuart Pimm, Akira Sasaki, Robert Ulanowicz, and Peter Yodzis for their helpful comments.
PY - 1989
Y1 - 1989
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.
KW - Aggregations
KW - Approximate aggregation
KW - Ecosystem
KW - Optimal dynamics
KW - Time scale
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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
SN - 1477-8599
VL - 6
SP - 1
EP - 23
JO - Mathematical Medicine and Biology
JF - Mathematical Medicine and Biology
IS - 1
ER -