International Encyclopedia of Systems and Cybernetics

2nd Edition, as published by Charles François 2004 Presented by the Bertalanffy Center for the Study of Systems Science Vienna for public access.


The International Encyclopedia of Systems and Cybernetics was first edited and published by the system scientist Charles François in 1997. The online version that is provided here was based on the 2nd edition in 2004. It was uploaded and gifted to the center by ASC president Michael Lissack in 2019; the BCSSS purchased the rights for the re-publication of this volume in 200?. In 2018, the original editor expressed his wish to pass on the stewardship over the maintenance and further development of the encyclopedia to the Bertalanffy Center. In the future, the BCSSS seeks to further develop the encyclopedia by open collaboration within the systems sciences. Until the center has found and been able to implement an adequate technical solution for this, the static website is made accessible for the benefit of public scholarship and education.


CRITICALITY (Self-organized) 1)2)

Condition of a "dynamical system with extended spatial degrees of freedom in two or three dimensions" which "naturally evolves into a self-organized critical state" (P. BAK, C. TANG & K. WIESENFELD, 1988, p.365).

The authors state:"By self organized we mean that the system naturally evolves to the state without detailed specification of the initial conditions (i.e. the critical state is an attractor of the dynamics). Moreover, the critical state is robust with respect to variations of parameters, and the presence of quenched randomness" (Ibid).

However more recently P. BAK and K. CHEN state; "… composite systems may never reach equilibrium but instead evolve from one meta stable state to the next" (1991, p. 26). They add:"During the past four years, experiments and models have demonstrated that many composite systems at the heart of geology, economy, biology, and meteorology show signs of self-organized criticality. These insights have improved our understanding of the behavior of the earth's crust, stock markets, ecosystems and many other composite systems" (Ibid).

Self-organized criticality has two "signatures" or "fingerprints" in P. BAK's and al. terms:

- a spatial ones which appears as a fractal structure specified by a power-law

- a temporal one which corresponds in each case to a specific flicker-noise

These abstract explanations become clearer when connected with ASHBY's concepts of ultrastability, non determined transformation and transition's probabilities matrix, all related to composite systems (See his :"Introduction to Cybernetics").

St. KAUFFMAN uses the criticality model in the co-evolution dynamics of populations (1993, p.256).

P. BAK comments: "… regularity of catastrophic events, fractals, 1/f noise, and Zipf's law – are so similar, in that they can all be expressed as straight lines on a double logarithmic plot, that they make us wonder if they are all manifestations of a single principle…. – Maybe self-organized criticality is that single underlying principle.

"Self-organized critical systems evolve to the complex critical state without interference from any outside agent.

The process of self-organization takes place over a very long transient period. Complex behavior, whether in geophysics of biology, is always created by a long process of evolution. It cannot be understood by studying the system within a time frame that is short compared with this evolutionary process. The phrase "you cannot understand the present without understanding history" takes on a deeper and more precise meaning (1996, p.31).

BAK also observes that "self-organized criticality can actually be thought of as the theoretical underpinning for catastrophism, the oposite philosophy to gradualism" (Ibid, p.131).

Both views are useful in their own way, for instance in evolution theory. BAK writes: "If the theory of self-organized criticlity is applicable, then the dynamics of avalanches represent the link between DARWIN's view of continuous evolution and the punctuations representing sudden quantitative and qualitative changes. Sandpiles are driven by small changes but they nevertheless exhibit large catastrophic events" (Ibid).


  • 1) General information
  • 2) Methodology or model
  • 3) Epistemology, ontology and semantics
  • 4) Human sciences
  • 5) Discipline oriented


Bertalanffy Center for the Study of Systems Science(2020).

To cite this page, please use the following information:

Bertalanffy Center for the Study of Systems Science (2020). Title of the entry. In Charles François (Ed.), International Encyclopedia of Systems and Cybernetics (2). Retrieved from www.systemspedia.org/[full/url]

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