BALANCING SURVIVAL AND EXTINCTION IN NONAUTONOMOUS COMPETITIVE LOTKA-VOLTERRA SYSTEMS WITH INFINITE DELAYS

摘要

The qualitative properties of certain type of nonautonomous competitive Lotka-Volterra systems with infinite delay are considered. By constructing suitable Lyapunov-type functional, we establish a series of easily verifiable algebraic conditions on the coefficients and the kernels, which are sufficient to ensure the extinction and survival of a determined number of species. The surviving part stabilizes around any solution of a subsystem of the systems in study. These conditions also guarantee the persistence, extreme stability and asymptotic behavior of the systems.%Lotka-Volterra system;extinction;competition;delay;persistence;extreme stability;global asymptotical stability