PERCOLATION
| Collection | International Encyclopedia of Systems and Cybernetics |
|---|---|
| Year | 2004 |
| Vol. (num.) | 2(2) |
| ID | ◀ 2522 ▶ |
| Object type | Methodology or model |
Propagation mode of a process in a medium or a relatively homogeneous system, characterized by a sudden discontinuity at some precise instant, depending on a critical density of the main component in that medium or system.
In random graphs used as models “…percolation thresholds occur … and determine when large, connected webs of elements will form. Below the threshold, such webs do not form; above the threshold, they do” (S. KAUFFMAN, 1993, p.205).
This is a dynamics of contagion and apply only to almost homogeneous systems. The concept was introduced by the English mathematician J.M. HAMMERSLEY in 1956, and corresponds to a general model which permits a better understanding of numerous phenomena, as for example:
- epidemics and epizootics
- forest and bush fires
- pest invasions in fields and orchards
- mud or rock slides, or snow avalanches
- the triggering phase of numerous chemical processes
On this side of a defined density of the principal component of the system or medium, the process remains confined and cannot propagate itself to the whole system.
P. GRASSBERGER, using the example of a specific pest invasion in an orchard planted with various kinds of trees, observes that: “One may ask oneself if the chances of a pest to invade one by one all of the apple trees do increase regularly with the proportion of apple trees…
- “Such is not the case. Quite surprisingly, the pests chances to run from one to the other extremity of the orchard are practically nil under a certain proportion of apple trees but become practically 100 percent over that value…
- “Percolation functions are like an ”all or nothing process“ (1991, p.640).
Of course, it is implied that no perturbing factor does interfere. The situation would by quite different if a strong wind should transport the insects far away (see “Oriented percolation”) or if the affected population members would be able to travel at great distances.