Convergence of solutions for Volterra–Lotka prey–predator systems with time delays

This work is concerned with NN-species prey–predator systems with time delays. The aim of this work is to obtain a sufficient condition for asymptotic behavior of the time-dependent solution and the existence of a positive steady-state solution. The result of global asymptotic stability implies that all of the model systems coexist; the trivial and all kinds of semitrivial solutions are unstable.