ERGODIC PROBLEM
| Collection | International Encyclopedia of Systems and Cybernetics |
|---|---|
| Year | 2004 |
| Vol. (num.) | 2(1) |
| ID | ◀ 1162 ▶ |
| Object type | General information, Methodology or model |
The difficulty to determine the nature of the behavior of a system depending of various ill-defined variables.
According to J.S. GRIFFITH this problem appears: “… when the long-term time average of a property of a dynamical system is equal to the average of that property over the phase space of the system” (1965, p.92).
While this is a problem that originates in classical mechanics, it becomes more and more important for complex systems, particularly those not very strongly integrated, as populations for instance. It is now clear that it has a close relation to networks behavior and to deterministic chaos, in accordance with H. POINCARÉ first inklings, when he considered the 3-bodies problem.
A basic character of networks is the presence of various simultaneous initially unconnected conditions, i.e. the basis for chaotic behavior.
All determinisms do not disappear in chaos and return of former states is always possible. However the \term“{long-term}” condition is of basic importance, because the reappearance of some specific state may need a very long span of time when the original conditions are numerous and out of phase on a considerable scale. Consequently, it may be very difficult to establish the ergodic character of a system's behavior.