Stability of model ecosystems with time-delay.

Abstract In this work, we attempt to formulize and partially resolve the “time-delay versus stability” as well as “complexity versus 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, we will show important structural properties of the density-dependent models with time-lag, and establish tolerance of community stability to a broad class of nonlinear interactions and to a class of time-delays.