A critical case for the spiral stability for \(2\times 2\) discontinuous systems and an application to recursive neural networks (Q346973)

This paper first provides a result on the assymptitic stability of the origin of a planar piecewise smooth differential system which are separated in four parts associated to the four quadrants under a very strong condition. Then applying this result to a recursive neural networks with nonlinear piecewise smooth activitations, the authors obtained some sufficient conditions on the assymptotic stability of the orgin of the networks.