STABILITY OF MODEL ECOSYSTEMS WITH TIME-DELAY

An attempt was made to formulate and partially resolve the time-delay vs. stability as well as complexity vs. stability problems in model ecosystems, in the framework of Lyapunov''s stability theory. Sufficient conditions are given for stability of models with time-lag under structural perturbations caused by nonlinear interactions among species in the community. As a byproduct of this analysis, important structural properties of the density dependent models with time-lag are shown and the tolerance of community stability to a broad class of nonlinear interactions and to a class of time-delays is established.