Practical measurement of complexity in dynamic systems

Abstract

Abstract A difficulty in complexity theory is lack of a clear definition for complexity, particularly one that is measurable. Those approaches that provide measurable definitions for the absolute complexity of a system often impose the requirement of perfect or near-perfect knowledge of system structure.In practice, it is intractable or impossible to measure the complexity of most dynamic systems.However, by measuring behavioral complexity in context with environmental scenarios, it is ossible to set bounds on a system's absolute (maximum) complexity and estimate its total complexity. As this paper shows, behavioral complexity can be determined by observing a system's changes in kinetic energy.This research establishes a methodology for measuring complexity in dynamic systems without the requirement of system structure knowledge. This measurement can be used to compare systems, understand system risks, determine failure dynamics, and guide system architecture.