Stability analysis for a single-species chemostat model with age structure and contribution of population to resource

摘要

In an ecosystem some populations not only consume the resource but also contribute themselves to the resource after senescence and other deaths and considered another source of resource. In view of these facts and based on whether the population individual is capable of reproduction, a single-species chemostat model with age structure and the contribution to resource is formulated and analyzed. We introduce two thresholds and α₀ by the method of next generation matrix and further obtain conditions of stability for equilibria. Our results indicate that the population can be eradicated if the input concentration of external resource α is controlled under a threshold α ₀. In addition, the results show that the contribution of population to resource make threshold value α ₀ larger, which implies, in view of the biological meaning, that such contribution plays a negative role in suppressing population. Keywords Chemostat - Stage structure - Next generation matrix - Global stability