Excerpt

The idea of cooperation has been an important element in societies for millennia. In fact, ancient Greek cooperative traditions incorporated an idea of self-organization that can still be found today, for example, as trade unions. Self-organized entities such as communities, cities, or even national states comprise elements in their substructure that typically interact in a nonlinear way. Such entities may be called complex systems. When the interaction of such sub-elements is strong enough and the environment of the system provides the suitable conditions, the system of interacting elements develops a novel common behavior. This process of new organization is called self-organization. Such self-organizing processes may not emerge only in societal systems (Smith and Stevens 1996), such as herd behavior or group thinking, but occur also in biological systems as animal stripe and spiral patterns (Turing 1952), in chemistry as self-assembly of molecules (Lehn 2002), and in human behavior as movement coordination (Kelso and Schöner 1988).

Theoretical models of each such self-organized system consider the nonlinear interaction of certain modes. Such modes capture the system-wide interactions and may represent spatial, temporal, or spatiotemporal patterns. Of course, the origin of these modes and their respective coupling is specific to each system. For instance, in physics the quantum-mechanical laser theory (Haken 1983) shows that the optical laser beam observed in experiments represents a stationary self-organized system state, which corresponds to a single oscillatory coherent mode that emerges from noncoherent modes by a state transition. Such transitions also describe the emergence of self-organized systems in nonphysical systems, as pointed out above.

Bibliography

Cassani, A., A. Monteverde, and M. Piumetti. 2021. “Belousov–Zhabotinsky Type Reactions: The Non-Linear Behavior of Chemical Systems.” Journal of Mathematical Chemistry 59:792–826. https://doi.org/10.1007/s10910-021-01223-9.

Childs, D. 2001. The Fall of the GDR. London, UK: Routledge.

Haken, H. 1983. Laser Theory. Heidelberg, Germany: Springer.

Hutt, A., A. Longtin, and L. Schimansky-Geier. 2007. “Additive Global Noise Delays Turing Bifurcations.” Physical Review Letters 98 (23): 230601. https://doi.org/10.1103/PhysRevLett.98.230601.

Jaeger, G. 1998. “The Ehrenfest Classification of Phase Transitions.” Archive for History of Exact Sciences 53:51–81. https://doi.org/10.1007/s004070050021.

Jirsa, V. K., J. A. S. Kelso, and A. Fuchs. 1999. “Traversing Scales of Brain and Behavioral Organization III: Theoretical Modeling.” In Analysis of Neurophysiological Brain Functioning, edited by C. Uhl. Springer Series in Synergetics. Berlin, Germany: Springer. https://doi.org/10.1007/978-3-642-60007-4_6.

Kelso, J. A. S., and G. Schöner. 1988. “Self-Organization of Coordinate Movement Patterns.” Human Movement Science 7 (1): 27–46. https://doi.org/10.1016/0167-9457(88)90003-6.

Kuramoto, Y. 1984. Chemical Oscillations, Eaves, and Turbulence. Vol. 19. Springer Series in Synergetics. Berlin, Germany: Springer. https://doi.org/10.1007/978-3-642-69689-3.

Lehn, J. M. 2002. “Toward Complex Matter: Supramolecular Chemistry and Self-Organization.” Proceedings of the National Academy of Sciences 99 (8): 4763–4768. https://doi.org/10.1073/pnas.072065599.

Mosekilde, E., and O. G. Mouritsen. 1995. Modelling the Dynamics of Biological Systems: Nonlinear Phenomena and Pattern Formation. Vol. 65. Springer Series in Synergetics. Berlin, Germany: Springer. https://doi.org/10.1007/978-3-642-79290-8.

Portugali, J. 2020. “Self-Organisation and the City.” In Synergetics, 2nd, edited by A. Hutt and H. Haken, 357–404. Encyclopedia of Complexity and Systems Science. New York, NY: Springer. https://doi.org/10.1007/978-3-642-27737-5_471-2.

Prigogine, I. 1981. From Being to Becoming: Time and Complexity in the Physical Sciences. San Francisco, CA: W. H. Freeman & Co. Ltd.

Smith, T. S., and G. T. Stevens. 1996. “Emergence, Self-Organization, and Social Interaction: Arousal-Dependent Structure in Social Systems.” Sociological Theory 14 (2): 131–153. https://doi.org/10.2307/201903.

Tschacher, W., G. Schiepek, and E. J. Brunner. 1992. Self-Organization and Clinical Psychology: Empirical Approaches to Synergetics in Psychology. Vol. 58. Springer Series in Synergetics. Berlin, Germany: Springer. https://doi.org/10.1007/978-3-642-77534-5.

Turing, A. M. 1952. “The Chemical Basis of Morphogenesis.” Philosophical Transactions of the Royal Society of London B 237 (641): 37–72. https://doi.org/10.1098/rstb.1952.0012.

Weidlich, W. 1994. “Synergetic Modelling Concepts for Sociodynamics with Application to Collective Political Opinion Formation.” The Journal of Mathematical Sociology 18 (4): 267–291. https://doi.org/10.1080/0022250X.1994.9990129.

Zhang, W.-B. 1991. Synergetics Economics: Time and Change in Nonlinear Economics. Vol. 53. Springer Series in Synergetics. Berlin, Germany: Springer. https://doi.org/10.1007/978-3-642-75909-3.

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