Almost Periodic Solution of a Population Model: via Spectral Radius of Matrix

In the present paper, some new results on the existence and uniqueness of almost periodic solution (?-periodic solution) are obtained for a delayed population model. The method is based on combining matrix’s spectral theory with the generalized Banach fixed point theory, which is different from the method employed in the literature. Due to employing the matrix’s spectral theory, the existence and stability conditions are given in terms of spectral radius of explicit matrices. The obtained sufficient conditions are much different from the conditions given by the algebraic inequalities. Our new results generalize the previous results in the literature.