Volume 5, Number 4, Fall 1997
GLOBAL ASYMPTOTIC STABILITY,
ADDITIVE NEURAL NETWORKS, AND
THE JACOBIAN CONJECTURE
Abstract. The Markus-Yamabe conjecture asks whether
an autonomous system which has a Jacobian matrix
Df(x) whose eigenvalues all have negative real part for all
x ∈ Rn and f(0) = 0 must be globally asymptotically stable.
The recent work on this problem is explained and new results
are offered. Weaker conditions are obtained to ensure global
stability for dimension two, and a connection to the theory of
neural networks is made.