Nonlinear dynamics of open marine population with space-limited recruitment: The case of mortality control

摘要

In this paper we develop a nonlinear extension for the open marine population model which has been proposed by Roughgarden et at. [Ecology 66 (1985) 54-67]. To avoid the negative population density, which is a drawback of the original model, we introduce a nonlinear mechanism that the mortality rate depends on the size of area occupied by the adult population. Then we give a rigorous mathematical framework to analyse the model equation, and we show sufficient conditions for stability and instability of the steady state. Our instability result suggests, as was proposed by Roughgarden et al., that there exists a sustained oscillation of the population density. (C) 2002 Elsevier Science (USA). All rights reserved. [References: 14]