Lotka-Volterra equations: Stability, decomposition, and aggregation

The major objective of this paper is to propose a new decomposition-aggregation framework for stability analysis of Lotka-Volterra equations employing the concept of vector Liapunov functions. Both the disjoint and the overlapping decompositions are introduced to increase flexibility in constructing Liapunov functions for the overall system. Our second objective is to initiate a study of Lotka-Volterra equations with non-linear time-varying coefficients, which may serve as more realistic models in applications. For this type of model, we derive stability conditions for nonnegative equilibria as well as outline a nonequilibrium analysis based upon the notion of ultimate boundedness of motions with respect to the nonnegative orthant of the state space. Both objectives of this paper are directed towards a better understanding of the intricate interplay between stability and structure in complex models represented by Lotka-Volterra equations.