International Encyclopedia of Systems and Cybernetics

"…a set of supplementary constraints that the solutions of differential equations must satisfy at all times" (T.F. ALLEN and T.B. STARR, 1982, p.262).

It appears from the context that these authors understand that each set of boundary conditions corresponds to a typical hierarchical level (p.44).

As stated by H. HAKEN, boundary conditions can be periodic (1983, p.269). Consequently, there are specific boundary variables which affect boundary conditions.

J. PLATT writes: "The surface may be taken as passing through a family of points where some parameter such as "interaction-density" has a maximum gradient" (1969, p.201-214).

Furthermore… "The boundary-surface for one property (such as heat-flows) will tend to coincide with the boundary surfaces for many other properties (such as blood flow, sensors endings, physical density, and so on) because the surfaces are mutually-reinforcing".

And… "All gradients and flows in the region very near the boundary will tend to be either parallel or perpendicular to the boundary… Evidently in the region close to a boundary the strong-coupling interactions within the systems are parallel to the boundary while the weaker-coupling interactions between the system and the larger super-system flow in and cut perpendicular to the boundary" (Ibid).

All this obviously applies to boundary conditions in social systems, as for example beehives, anthills, business companies or nations.

A very important observation by I. PRIGOGINE et al. is that: "A sufficiently small system will always be dominated by the boundary conditions – the conditions imposed at the walls of the vessel (note: the authors are refering in this specific case to a chemical reaction. Similar effects are however present whenever boundaries are proportionally very important in relation to surface and volume)." In order for the nonlinearities to be able to lead to a choice between various possible solutions, it is necessary to go beyond some critical spatial dimensions. Only then can the system acquire a degree of autonomy with respect to the outside world" (1975, p.31). This is because: "In the case of small-size fluctuations , boundary effects will dominate and fluctuations will regress" (Ibid, p.43).

This aspect is probably the most basic explanation of the universal tendency of systems – natural or artificial – to grow in size, at least up to some critical limit where the effects of big size become preponderantly negative.

Boundary conditions are not necessarily constant. A.S. IBERALL states: "… if boundary conditions of a nonconstant nature are maintained, the system may find a process which is either in steady state or which is dynamically fluctuating… It has begun to be realized that fluctuations and turnover are necessary conditions for the maintenance of form (See e.g. the work of PRIGOGINE, KATCHALSKY, MOROWITZ, PATTEE, IBERALL, ZHABOTINSKY)" (1973, p.5).

Such concepts were developped as early as 1942 by the French engineer Ch LAVILLE in his theory of vortexes.