  In this paper, we exploit the fact that the dynamics of homogeneous and
isotropic Friedmann-Lemaitre universes is a special case of generalized
Lotka-Volterra system where the competitive species are the barotropic fluids
filling the Universe. Without coupling between those fluids, Lotka-Volterra
formulation offers a pedagogical and simple way to interpret usual
Friedmann-Lemaitre cosmological dynamics. A natural and physical coupling
between cosmological fluids is proposed which preserve the structure of the
dynamical equations. Using the standard tools of Lotka-Volterra dynamics, we
obtain the general Lyapunov function of the system when one of the fluids is
coupled to dark energy. This provides in a rigorous form a generic asymptotic
behavior for cosmic expansion in presence of coupled species, beyond the
standard de Sitter, Einstein-de Sitter and Milne cosmologies. Finally, we
conjecture that chaos can appear for at least four interacting fluids.
