Global Stability in Ecological Models with Continuous Time Delays

摘要

This model examines the stability properties of a general system of first-order integro-differential equations which describe the dynamics of interacting species populations. A sufficient condition for the global stability of an equilibrium state is derived. This condition is an improvement over the condition derived by Woerz-Busekros (1978) for similar equations in that this condition has intuitive biological interpretations and is verifiable in a finite number of arithmetical steps. This condition is shown to be both necessary and sufficient for global asymptotic stability of the equilibrium for communities of mutualistically interacting species. Application of the results to an ecological system is also provided. (ERA citation 05:001767)