The usefulness of the Lempel-Ziv complexity and the Lyapanov exponent as two metrics to characterize the dynamic patterns is studied. System output signal is mapped to a binary string and the complexity measure of the time-sequence is computed. Along with the complexity we use the Lyapunov exponent to evaluate the order and disorder in the nonlinear systems. Results from the Lempel-Ziv complexity are compared with the results from the Lyapunov exponent computation. Using these two metrics, we can distinguish the noise from chaos and order. In addition, using same metrics we study the complexity measure of the Fibonacci map as a quasiperiodic system. Our analytical and numerical results prove that for a system like Fibonacci map, complexity grows logarithmically with the evolutionary length of the data block. We conclude that the normalized Lempel-Ziv complexity measure can be used as a system classifier. This quantity turns out to be 1 for random sequences and non-zero value less than 1 for chaotic sequences. While for periodic and quasiperiodic responses as data string grows, their normalized complexity approaches zero. However, higher deceasing rate is observed for periodic responses.
Skip Nav Destination
e-mail: davouda@engr.subr.edu
Article navigation
July 2008
Research Papers
Measures of Order in Dynamic Systems
Davoud Arasteh
Davoud Arasteh
Department of Electronic Engineering Technology,
e-mail: davouda@engr.subr.edu
Southern University
, Baton Rouge, LA 70813
Search for other works by this author on:
Davoud Arasteh
Department of Electronic Engineering Technology,
Southern University
, Baton Rouge, LA 70813e-mail: davouda@engr.subr.edu
J. Comput. Nonlinear Dynam. Jul 2008, 3(3): 031002 (10 pages)
Published Online: April 30, 2008
Article history
Received:
September 17, 2006
Revised:
October 17, 2007
Published:
April 30, 2008
Citation
Arasteh, D. (April 30, 2008). "Measures of Order in Dynamic Systems." ASME. J. Comput. Nonlinear Dynam. July 2008; 3(3): 031002. https://doi.org/10.1115/1.2908174
Download citation file:
Get Email Alerts
Cited By
A Comparative Analysis Among Dynamics Modeling Approaches for Space Manipulator Systems
J. Comput. Nonlinear Dynam (January 2025)
A Finite Difference-Based Adams-Type Approach for Numerical Solution of Nonlinear Fractional Differential Equations: A Fractional Lotka–Volterra Model as a Case Study
J. Comput. Nonlinear Dynam (January 2025)
Nonlinear Dynamic Analysis of Riemann–Liouville Fractional-Order Damping Giant Magnetostrictive Actuator
J. Comput. Nonlinear Dynam (January 2025)
Related Articles
Introduction
J. Comput. Nonlinear Dynam (October,2006)
On the Global Analysis of a Piecewise Linear System that is excited by a Gaussian White Noise
J. Comput. Nonlinear Dynam (September,2016)
Implementation of Periodicity Ratio in Analyzing Nonlinear Dynamic Systems: A Comparison With Lyapunov Exponent
J. Comput. Nonlinear Dynam (January,2008)
Shil’nikov Analysis of Homoclinic and Heteroclinic Orbits of the T System
J. Comput. Nonlinear Dynam (April,2011)
Related Proceedings Papers
Related Chapters
Ultra High-Speed Microbridge Chaos Domain
Intelligent Engineering Systems Through Artificial Neural Networks, Volume 17
Computing Algorithmic Complexity Using Advance Sampling Technique
Intelligent Engineering Systems through Artificial Neural Networks Volume 18
Boundary Layer Phenomenon for the Nonlinear Dynamical Systems with High-Speed Feedback
International Conference on Advanced Computer Theory and Engineering, 4th (ICACTE 2011)