Nonlinear character dependent models with constant time delay in population dynamics

A nonlinear character dependent model with constant time delay that extends the linear model of W. S. C. Gurney and R. M. Nisbet is introduced as a result of making the birth and death moduli dependent upon the total population. We reduce this model—an initial boundary value problem—to the solution of a pair of coupled nonlinear functional equations. Under suitable conditions, we establish the local existence, uniqueness, and continuation of solutions for all positive time. We also establish necessary and sufficient conditions for the local stability of time independent solutions in the form of a Lotka type characteristic equation similar to M. E. Gurtin and R. C. MacCamy's charateristic equation arising from their nonlinear extension of the age dependent MacKendrick-Von Foerster model.