Stability results for a size-structured population model with resources-dependence and inflow

It is undoubted that the survival of individuals of populations is dependent on resources (e.g., foods). We formulate a system of integro-differential equations to model the dynamics of a size-structured and resources-dependent population, a kind of inflow of newborn individuals from external environment is considered. The resource-dependence is incorporated through the size growth, mortality, fertility and feeding rates of the target population. The existence of the stationary size distributions are discussed, and the linear stability is investigated by means of the semigroup theory and the characteristic equation technique, some sufficient conditions for stability/instability of stationary states are obtained, and two examples and the corresponding simulations are presented.