Asymptotic spatial homogeneity in periodic quasimonotone reaction–diffusion systems with a first integral Original Research Article

The asymptotic spatial homogeneity of nonnegative solutions to a ττ-periodic quasimonotone reaction–diffusion-type initial-boundary value problem is established, provided the system possesses a first integral. The infinite-dimensional dynamical system generated by the system of PDEs is monotone but not strongly monotone. Results combining simple monotonicity with infinite dimensionality have not appeared in the literature. We apply our result to a cooperative Lotka–Volterra system with spatial diffusion.