S Shaped growth followed by decline
Posted: Sat Apr 10, 1999 4:25 pm
Dear John,
the scenario you describe reminds me much of the graphs process
in the case "Success to the Successful":
S-shaped growth: Far from their capacity boundary more or less
strong (logistic) growth is to be observed with all parties involved.
However at this stage the competition effect already affects all
competitors, particularly those who are at a disadvantage (e.g. due
to smaller growth rates).
Exponential decay: If the general capacity boundary is near, the
most successful competitor continues to grow at the expense of
the others.
Such a behaviour (including a coarse model) is described e.g. by
Bossel H.: Modellbildung und Simulation. 2. Auflage, Vieweg-
Verlag, Braunschweig/Wiesbaden 1994, pp. 290-291
Beltrami E.: Mathematics for Dynamic Modeling. Academic Press,
Orlando/London 1987, pp. 69-70
Regards,
Thorsten Rueffer
_________________________________________________________
Otto-Friedrich-Universitaet Bamberg
Lehrstuhl fuer Wirtschaftsinformatik,
insbes. Industrielle Anwendungssysteme
Dipl.-Wirtsch.Inf. Thorsten Rueffer
Feldkirchenstr. 21, D-96045 Bamberg
Tel.: (++49) 951/863-2540
Fax: (++49) 951/863-2680
thorsten.rueffer@sowi.uni-bamberg.de
the scenario you describe reminds me much of the graphs process
in the case "Success to the Successful":
S-shaped growth: Far from their capacity boundary more or less
strong (logistic) growth is to be observed with all parties involved.
However at this stage the competition effect already affects all
competitors, particularly those who are at a disadvantage (e.g. due
to smaller growth rates).
Exponential decay: If the general capacity boundary is near, the
most successful competitor continues to grow at the expense of
the others.
Such a behaviour (including a coarse model) is described e.g. by
Bossel H.: Modellbildung und Simulation. 2. Auflage, Vieweg-
Verlag, Braunschweig/Wiesbaden 1994, pp. 290-291
Beltrami E.: Mathematics for Dynamic Modeling. Academic Press,
Orlando/London 1987, pp. 69-70
Regards,
Thorsten Rueffer
_________________________________________________________
Otto-Friedrich-Universitaet Bamberg
Lehrstuhl fuer Wirtschaftsinformatik,
insbes. Industrielle Anwendungssysteme
Dipl.-Wirtsch.Inf. Thorsten Rueffer
Feldkirchenstr. 21, D-96045 Bamberg
Tel.: (++49) 951/863-2540
Fax: (++49) 951/863-2680
thorsten.rueffer@sowi.uni-bamberg.de