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The search for universal laws that help establish a relationship betweendynamics and computation is driven by recent expansionist initiatives inbiologically inspired computing. A general setting to understand both suchdynamics and computation is a driven dynamical system that responds to atemporal input. Surprisingly, we find memory-loss a feature of driven systemsto forget their internal states helps provide unambiguous answers to thefollowing fundamental stability questions that have been unanswered fordecades: what is necessary and sufficient so that slightly different inputsstill lead to mostly similar responses? How does changing the driven system'sparameters affect stability? What is the mathematical definition of theedge-of-criticality? We anticipate our results to be timely in understandingand designing biologically inspired computers that are entering an era ofdedicated hardware implementations for neuromorphic computing andstate-of-the-art reservoir computing applications.

Stability and Memory-loss go Hand-in-Hand: Three Results in Dynamics & Computation