SEPARATRIX
Charles François (2004). SEPARATRIX, International Encyclopedia of Systems and Cybernetics, 2(2): 3022.
| Collection | International Encyclopedia of Systems and Cybernetics |
|---|---|
| Year | 2004 |
| Vol. (num.) | 2(2) |
| ID | ◀ 3022 ▶ |
| Object type | Methodology or model |
The boundary between basins of attraction, i. e. between two zones of stability of different characteristics.
R.H. ABRAHAM and C.D. SHAW state: “By definition, separatrix points are not in basins. Thus, they belong to the insets of limit sets which are not attractors, the exceptional limit sets” (1987, p.549).
As a result, the separatrix corresponds to the critical threshold, the locus where bifurcations can take place.
As stated by St. KAUFFMAN, in two dimensions, the separatrix is a line (i.e. one-dimensional), and in three dimensions it is a surface (i.e. bi-dimensional) (1993, p.176-7).