Measuring Complexity of Chaotic Systems With Cybernetics Applications

Measuring Complexity of Chaotic Systems With Cybernetics Applications

Nithin Nagaraj (National Institute of Advanced Studies, India) and Karthi Balasubramanian (Amrita University, India)
Copyright: © 2017 |Pages: 34
DOI: 10.4018/978-1-5225-2498-4.ch015
OnDemand PDF Download:
$30.00
List Price: $37.50

Abstract

Measuring complexity of systems is very important in Cybernetics. An aging human heart has a lower complexity than that of a younger one indicating a higher risk of cardiovascular diseases, pseudo-random sequences used in secure information storage and transmission systems are designed to have high complexity (to resist malicious attacks), brain networks in schizophrenia patients have lower complexity than corresponding networks in a healthy human brain. Such systems are typically modeled as deterministic nonlinear (chaotic) system which is further corrupted with stochastic noise (Gaussian or uniform distribution). After briefly reviewing various complexity measures, this chapter explores characterizing the complexity of deterministic nonlinear chaotic systems (tent, logistic and Hénon maps, Lorenz and Rössler flows) using specific measures such as Lempel-Ziv complexity, Approximate Entropy and Effort-To-Compress. Practical applications to neuron firing model, intra-cranial pressure monitoring, and cardiac aging detection are indicated.
Chapter Preview
Top

Complex Systems

A complex system is defined as one in which the individual components that make up the system are by themselves simple but which produces complex behavior due to varied interactions amongst themselves (Northrop, 2010). The study of complex systems has been nascent in the past and has come to prominence only in the last couple of decades. This has been made largely possible by the availability of high-end tools for high speed computation and analysis.

Complex systems possess some basic properties, listed below (Lloyd, 2001).

  • They are composed of simple components.

  • The interactions among components happen in a non-linear fashion.

  • Control of the systems is not centralized.

  • The systems show evolution and learning and adapt to improve themselves.

Some examples of naturally occurring complex systems include brain, immune system and respiratory system to name a few. A healthy human heart is known to produce complex beat-to-beat variations. Brain networks in schizophrenia patients have lower complexity than corresponding networks in a healthy human brain. In the physical world, complex systems are frequently encountered in fields like dynamics, information processing, cryptographic protocols, weather prediction, computation and study of population and evolution. For example, pseudo-random sequences used in secure information storage and transmission systems are designed to have high complexity (to resist malicious attacks). What makes complex systems really interesting is that they exhibit some very interesting behavior, even though the underlying equations may well be simple and deterministic.

Complete Chapter List

Search this Book:
Reset