Dynamical Systems that Heal

Abstract

Malware plays a key role in attacking critical infrastructure. With this problem in mind, we introduce systems that heal from a broader perspective than the standard digital computer model: Our goal in a more general theory is to be applicable to systems that contain subsystems that do not solely rely on the execution of register machine instructions. Our broader approach assumes a dynamical system that performs tasks. Our primary contribution defines a principle of self-modifiability in dynamical systems and demonstrates how it can be used to heal a malfunctioning dynamical system. As far as we know, to date there has not been a mathematical notion of self-modifiability in dynamical systems; hitherto there has not been a formal system for describing how to heal damaged computer instructions or to heal differential equations that perform tasks.