Global dynamics for Lotka–Volterra systems with infinite delay and patch structure

We study some aspects of the global dynamics of an n-dimensional Lotka–Volterra system with infinite delay and patch structure, such as extinction, persistence, existence and global asymptotic stability of a positive equilibrium. Both the cases of an irreducible and reducible linear community matrix are considered, and no restriction on the signs of the intra- and inter-specific delayed terms is imposed. Although the system is not cooperative, our approach often uses comparative results with an auxiliary cooperative system. Some models in recent literature are generalized, and results improved.