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Volume 5,     Number 4,     Fall 1997

 

GLOBAL ASYMPTOTIC STABILITY,
ADDITIVE NEURAL NETWORKS, AND
THE JACOBIAN CONJECTURE
MARC CHAMBERLAND

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 xRn 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.

 

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