Abstract :
In this paper we develop a nonlinear extension for the open marine population model
which has been proposed by Roughgarden et al. [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.
2002 Elsevier Science (USA). All rights reserved.
