Computing with transiently stable states

Abstract

Stability is an essential constraint in the design of linear dynamical systems. Similar stability restrictions on nonlinear dynamical systems, such as echo state network, have been enforced in order to use them for reliable computation. In this paper we introduce a novel computational mode for nonlinear systems with sigmoidal nonlinearity, which does not require global stability. In this mode, although the autonomous system is unstable, the input signal forces the system dynamics to become "transiently stable". We demonstrate with a function approximation experiment that the transiently stable system can still do useful computation. We explain the principles of computation with the stability of local dynamics obtained from linearization of the system at the operating point.