  The search for universal laws that help establish a relationship between
dynamics and computation is driven by recent expansionist initiatives in
biologically inspired computing. A general setting to understand both such
dynamics and computation is a driven dynamical system that responds to a
temporal input. Surprisingly, we find memory-loss a feature of driven systems
to forget their internal states helps provide unambiguous answers to the
following fundamental stability questions that have been unanswered for
decades: what is necessary and sufficient so that slightly different inputs
still lead to mostly similar responses? How does changing the driven system's
parameters affect stability? What is the mathematical definition of the
edge-of-criticality? We anticipate our results to be timely in understanding
and designing biologically inspired computers that are entering an era of
dedicated hardware implementations for neuromorphic computing and
state-of-the-art reservoir computing applications.
