Discrete infinite-dimensional type-\(K\) monotone dynamical systems and time-periodic reaction--diffusion systems.
The authors study the asymptotic behavior of discrete type-\(K\) monotone dynamical systems and time-periodic reaction-diffusion systems, by using the index theory for fixed points, permanence, global stability, convergence everywhere and coexistence. The results can be used to establish the sufficient conditions for the systems to persist uniformly and the convergence results for all orbits. As applications, time-periodic Lotka-Volterra systems with diffusion are considered and sufficient conditions for such systems to have a unique positive solution are given. So the main results of this paper are interesting and nice.
scientific article; zbMATH DE number 1901951
scientific article