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.


STABILITY (Structural) 2)

"The capacity of a system to maintain the same essential patterns of behavior despite some modification in the structural interrelations between the systems parts" (T.F.H. ALLEN &.T.B. STARR, 1982, p.278).

The concept of structural stability was introduced in 1937 by the Russian mathematicians A. ANDRONOV and L. PONTRIAGIN. It led and is still leading to considerable developments in the topological study of the complex systems stabilility, as for example catastrophe theory (THOM and ZEEMAN), the various types of attractors, and deterministic chaos.

As stated by L. LÖFGREN: "A system is structurally stable if the topology of its trajectories is preserved under sufficiently small perturbations" (1974, p.78).

For K.B.DE GREENE: "A function or system is structurally stable if such qualitative properties as numbers and kind of critical points and basins of attraction remain unchanged after a sufficiently small perturbation" (1990, p.54).

Small modifications correspond mostly to small perturbations. Structural stability is compatible with more or less periodic changes of state, i.e. with ergodicity.

According to S. DINER: "A structurally stable dynamic system is… a topologically stable system, i.e. a system whose phase portrait undergoes few modifications and remains topologically self-similar under the influence of lesser perturbations in its movement equations… ; (it) maintains its essential qualitative properties when affected by a slight perturbation" (1992, p.360).

This is the case for merely local instabilities.

To the ALLEN and STARR's definition and LÖFGREN's comment, which correspond to confirmed stable systems, one should aggregate the following comment by K.DE GREENE: "… structural stability in dissipative-structure theory refers to the response of the system to the addition of new elements" (1988, p. 291).

And: "The structural stability of any existing deterministic system, potentially capable of evolution, is continually tested by both internal and external (random noise) fluctuations" (DE GREENE, 1994, p.14). On the contrary: "The system is structurally unstable if mutations (genetic, scientific, technological, "great persons" – my terms) can multiply and take over and modify system processes" (Ibid).

R. ROSEN sees a practical use for the concept: "Structural stability is a general framework for comparing one description of a class of objects against another description, usually in terms of measures of closeness" (1991b, p.480).


  • 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]

We thank the following partners for making the open access of this volume possible: