- ▪P. de Leenheer, D. Angeli, E.D. Sontag, "On predator-prey systems and small-gain theorems", Math. Biosci. Eng., vol. 2, no. 1, pp. 25–42, 2005. pdf
Abstract
This paper deals with an almost global attractivity result for Lotka-Volterra systems with predator-prey interactions. These systems can be written as (negative) feedback systems. The subsystems of the feedback loop are monotone control systems, possessing particular input-output properties. We use a small-gain theorem, adapted to a context of systems with multiple equilibrium points to obtain the desired almost global attractivity result. It provides sufficient conditions to rule out oscillatory or more complicated behavior which is often observed in predator-prey systems.
- ▪D. Angeli, P. de Leenheer, E.D. Sontag, "A small-gain theorem for almost global convergence of monotone systems", Systems Control Lett., vol. 52, no. 5, pp. 407–414, 2004. pdf
Abstract
A small-gain theorem is presented for almost global stability of monotone control systems which are open-loop almost globally stable, when constant inputs are applied. The theorem assumes "negative feedback" interconnections. This typically destroys the monotonicity of the original flow and potentially destabilizes the resulting closed-loop system.
- ▪P. de Leenheer, D. Angeli, E.D. Sontag, "A feedback perspective for chemostat models with crowding effects", In Positive systems (Rome, 2003), pp. 167–174, 2003.
- ▪P. de Leenheer, D. Angeli, E.D. Sontag, "Small-gain theorems for predator-prey systems", In Positive systems (Rome, 2003), pp. 191–198, 2003.