Aggregate models of liquidity-profit dynamics

Michal Demetrian and Rudolf Zimka

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Abstract: We discuss the problem of limit cycles in an aggregate-type models of liquidity growth proposed and studied both theoretically and numerically by W. Semmler and M. Sieveking in \cite{SemmlerSieveking}. Their model is locally of predator-prey type with cannibalism in predator (profit) and logistic bound on prey's population (liquidity). We modify the model to include the weak Allee effect in liquidity and to study the local bifurcations of equilibria and limit cycles by means of the Hopf-Andronov theory. The main motivation for this study follows the economic theory of the so-called corridors of stability introduced by Leijonhuvud in \cite{Leijonh}. Similar importance of these effects is, however, found also in the originally developed dynamical models in biology, especially in mathematical ecology.

Date: 2026-07
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