Cooperative Systems and Time-Varying Discrete Diffusion for Single Species

w x The theory of monotone dynamical systems developed by Hirsch 2 has proved to be very successful in the study of the asymptotic behavior of solutions of competitive and cooperative systems of differential equations. w x w x Recently, Smith 4 and Takac 5]7 have partially extended some of Hirsch’s results in order to study non-autonomous periodic equations. In this article we complement some of Smith and Takac results that are applied in order to study a model for single-species non-linear discrete diffusion with time-varying coefficients. Models for single-species linear w x discrete diffusion were studied in 1, 3 obtaining results about extinction and persistence of the species. The systems studied in these articles are of the form