GROWTH-RATE PARAMETER
| Collection | International Encyclopedia of Systems and Cybernetics |
|---|---|
| Year | 2004 |
| Vol. (num.) | 2(1) |
| ID | ◀ 1494 ▶ |
| Object type | Methodology or model |
The factor which controls Template:Ency term.
Since no growth Template:Ency term is independent of its Template:Ency term conditions and/or intrinsic characteristics, none can be Template:Ency term at Template:Ency term. This must be reflected into growth equations if real Template:Ency term are to be satisfactorily modelled.
Thus a growth-rate parameter must be introduced into the equation.
According to Template:Ency person: “In the physical systems from which these equations were borrowed, that parameter corresponded to the amount of heating, or the amount of friction, or the amount of some other ”messy“ quantity. In short, the amount of Template:Ency term” (1987, p.63).
Template:Ency person uses as an example a very simple difference equation:
He writes: “The Template:Ency term of x$_{n}$ generated by this single algebraic equation exhibits an extraordinary Template:Ency term from Template:Ency term to Template:Ency term as the parameter a, which measures the strength of Template:Ency term is increased” (1987, p.170).
For x included between 0 and 1 and for different values of a, Template:Ency person distinguishes the following cases:
- for a = 1 — Growth followed by monotonic damping and extinction;
- for a = 2,9 Growth toward an Template:Ency term with a punctual Template:Ency term (variable according to the value of a);
- for a = 3,2 Growth followed by Template:Ency term around a Template:Ency term;
- for a = 4,0 Growth followed by apparently Template:Ency term.
For a clearer understanding, see reference.