The stability of interacting populations

An estimate of the decay constant indicates faster convergence to the steady state the larger the size of the equilibrium populations, the intra- species interaction, and the ‘ nutritional value ’ of the inter-species interaction.

Abstract

Abstract A general Volterra model for describing the dynamics of interacting populations is proven to be inherently stable. Conditions are given under which, for any particular application of the model, each species in the community will either oscillate about its unique equilibrium value continuously in a limit cycle or approach it asymptotically. The asymptotic approach to the steady state is proven to be exponential eventually. An estimate of the decay constant indicates faster convergence to the steady state the larger the size of the equilibrium populations, the intra-species interaction, and the ‘ nutritional value ’ of the inter-species interaction.