Dynamical analysis on a size-structured population model of Daphnia with delayed birth process

Abstract

In this paper, we investigate a size-structured population model of Daphnia coupled with an unstructured algal food source. We introduce a delay into the boundary condition of this model, where the delay describes the effect of competition for finding food or resource in short supply juvenile period. Following the semigroup theory, we transform our model into the abstract boundary delay problem and obtain the existence and uniqueness of a positive stationary solution. By means of the spectral analysis and the characteristic equation technique, the instability and linear stability results of stationary solutions are formulated in terms of the basic reproduction number ℛ(F). Some numerical simulation examples are presented to illustrate the feasibility of our main results.