Almost Global Convergence in Singular Perturbations of Strongly Monotone Systems

TL;DR

This paper investigates the conditions under which singular perturbations of strongly monotone systems still exhibit global convergence to equilibria, extending Hirsch's convergence theorem.

Contribution

It extends Hirsch's generic convergence theorem to singular perturbations of monotone systems, providing new insights into their stability behavior.

Findings

Global convergence is preserved under certain singular perturbations.

Theoretical conditions for convergence in perturbed systems are established.

Results enhance understanding of stability in complex dynamical systems.

Abstract

This paper deals with global convergence to equilibria, and in particular Hirsch's generic convergence theorem for strongly monotone systems, for singular perturbations of monotone systems.