Evolution model with a cumulative feedback coupling.
The paper is concerned with a toy model that generalizes the standard Lotka-Volterra equation for a certain population by introducing a competition between instantaneous and accumulative, history-dependent nonlinear feedback the origin of which could be a contribution from any kind of mismanagement in the past. The results depend on the sign of that additional cumulative loss or gain term of strength lambda. In case of a positive coupling the system offers a maximum gain achieved after a finite time but the population will die out in the long time limit. In this case the instantaneous loss term of strength u is irrelevant and the model exhibits an exact solution. In the opposite case lambda<0 the time evolution of the system is terminated in a crash after t(s) provided u=0. This singularity after a finite time can be avoided if u not equal to 0. The approach may well be of relevance for the qualitative understanding of more realistic descriptions.
Trimper
Steffen
S
Fachbereich Physik, Martin-Luther-Universität Halle, D-06099 Halle, Germany.
Zabrocki
Knud
K
Schulz
Michael
M