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.
N. Nagaraj and Dr. Karthi Balasubramanian, “Measuring Complexity of Chaotic Systems With Cybernetics Applications”, in Handbook of Research on Applied Cybernetics and Systems Science, 2017, pp. 301-334.