Global stability of a two-species piecewise linear volterra ecosystem

This paper extends the results of Goh 1], and Takeuchi and Adachi 2,3] concerning the generalized linear Volterra model. We introduce a piecewise linear Volterra model for a two- species system. The solution of the steady-state problem is then shown to be equivalent to finding the solution to the Generalized Linear Complementarity Problem. We show when this nonnegative equilibrium is unique and globally asymptotically stable in the sense of Goh 1].