Abstract
Hierarchical organization is typical of complex living systems. Hierarchies of two kinds should be distinguished. Evolutionary hierarchies, such as genealogical trees, are memories of a branching process. The degree of kinship represents a natural measure of distance between elements in such trees, leading to the concept of an ultrametric space. Dynamical hierarchies are formed by coexisting structures of different levels that interact to determine the system’s dynamics.
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References
R. Rammal, G. Toulouse, M.A. Virasoro, Rev. Mod. Phys. 58, 765 (1986)
H.A. Ceccatto, B.A. Huberman, Physica Scripta 37, 145 (1988)
D. Sherrington, S. Kirkpatrick, Phys. Rev. Lett. 35, 1972 (1975)
N. Metropolis, A.W. Rosenblueth, M.N. Rosenblueth, A.H. Teller, J. Chem. Phys. 6, 1087 (1953)
V. Dotsenko, An Introduction to the Theory of Spin Glasses and Neural Networks (World Scientific, Singapore 1994)
K.H. Fischer, J.A. Hertz, Spin Glasses (Cambridge University Press, Cambridge 1991)
S.F. Edwards, P.W. Anderson, J. Phys. F 5, 965 (1975)
G. Parisi, J. Phys. A 13, 1887 (1980)
G. Parisi, Phys. Rev. Lett. 50, 1946 (1983)
M. Mezard, G. Parisi, M. Virasoro, Spin-Glass Theory and Beyond (World Scientific, Singapore 1987)
A.P. Young, Phys. Rev. Lett. 51, 1206 (1983)
R.N. Bhatt, A.P. Young, J. Magn. Magn. Mater. 54–57, 191 (1986)
S.C. Manrubia, A.S. Mikhailov, Europhys. Lett. 50, 580 (2000)
S.C. Manrubia. U. Bastolla, A.S. Mikhailov, Eur. Phys. J. B 23, 497 (2001)
A.N. Kolmogorov, C. R. Acad. Sci. USSR 30, 301 (1941); 32, 16 (1941)
L.D. Landau, E.M. Lifshitz, Fluid Mechanics (Pergamon Press, New York 1987)
U. Frisch, Turbulence: The Legacy of A.N. Kolmogorov (Cambridge University Press, Cambridge 1995)
A.S. Mikhailov, D.H. Zanette, unpublished
J.D. Murray, Mathematical Biology (Springer, Berlin 1989)
R.J. Britten, E.H. Davidson, Science 165, 349 (1969)
E. Davidson, R.J. Britten, Science 204, 1052 (1976)
J. Monod, F. Jacob, Cold Spring Harbor Symp. Quant. Biol. 26, 389 (1961)
B.C. Goodwin, Adv. in Enzyme Regulation 3, 425 (1965)
B. Alberts, D. Bray, J. Lewis, M. Raff, K. Roberts, J.D. Watson, Molecular Biology of the Cell (Garland, New York 1994)
S.A. Kauffman, The Origins of Order — Self-Organization and Selection in Evolution (Oxford University Press, New York 1993)
R.M. May, Stability and Complexity in Model Ecosystems (Princeton University Press, Princeton, NJ 1973)
J. Hofbauer, K. Sigmund, Evolutionstheorie und dynamische Systeme — Mathematische Aspekte der Selektion (Paul Parey, Berlin 1984)
S.A.L.M. Kooijman, M.P. Boer, Dynamics Energy Budgets in Biological Systems: Theory and Applications in Ecotoxicology (Cambridge University Press, Cambridge 1993)
L. Edelstein-Keshet, Mathematical Models in Biology (Random House, New York 1988)
H.L. Smith, P. Waltman, The Theory of the Chemostat (Cambridge University Press, Cambridge 1994)
D. Ludwig, SIAM J. Appl. Math. 55, 564 (1995)
M. Giampietro, Agriculture, Ecosystems and Environment 65, 201 (1997)
R.U. Ayres, Resources, Environment and Economics: Applications of the Materials/Energy Balance Principle (John Wiley & Sons, New York 1978)
R.U. Ayres, P.M. Weaver, Eco-restructuring: Implications for Sustainable Development (United Nations University Press, Tokyo 1998)
C.S. Holling, “The Resilience of Terrestrial Ecosystems: Local Surprise and Global change”, In Sustainable Development of the Biosphere, eds. W.C. Clark, R.E. Munn (1986)
B.A. Huberman, T. Hogg, “The Behaviour of Computational Ecologies” In The Ecology of Computation, ed. B.A. Huberman (Elsevier, North-Holland 1988) p. 77–115
A.S. Mikhailov, Foundations of Synergetics I. Distributed Active Systems, 2nd revised edn. (Springer, Berlin 1990; 1995)
S. Galluccio, J.-P. Bouchaud, M. Potters, Phvsica A 259, 449 (1998) .
A. Gábor, I. Kondor, Physica A 274, 229 (1999)
R. Axelrod, D.S. Bennett, British J. Political Sci. 23, 211 (1993)
S. Galam, J. Math. Phychol. 30, 426 (1986)
S. Galam, J. Stat. Phys. 61, 943 (1990)
S. Galam, Physica A 274, 132 (1999)
R.N. Mantegna, Eur. Phys. J. B 11, 193 (1999)
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Mikhailov, A.S., Calenbuhr, V. (2002). Hierarchical Organization. In: From Cells to Societies. Springer Series in Synergetics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05062-0_8
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