scholarly journals HUFFMAN CODING AS A NONLINEAR DYNAMICAL SYSTEM

2011 ◽  
Vol 21 (06) ◽  
pp. 1727-1736 ◽  
Author(s):  
NITHIN NAGARAJ
Keyword(s):  
Lyapunov Exponent ◽  
Measurement Problem ◽  
Piecewise Linear ◽  
Nonlinear Dynamical System ◽  
Huffman Coding ◽  
Essential Information ◽  
Nonlinear Dynamical ◽  
Still Image ◽  
Binary Coding ◽  
Stochastic Sources

In this paper, source coding or data compression is viewed as a measurement problem. Given a measurement device with fewer states than the observable of a stochastic source, how can one capture their essential information? We propose modeling stochastic sources as piecewise-linear discrete chaotic dynamical systems known as Generalized Luröth Series (GLS) which has its roots in Georg Cantor's work in 1869. These GLS are special maps with the property that their Lyapunov exponent is equal to the Shannon's entropy of the source (up to a constant of proportionality). By successively approximating the source with GLS having fewer states (with the nearest Lyapunov exponent), we derive a binary coding algorithm which turns out to be a rediscovery of Huffman coding, the popular lossless compression algorithm used in the JPEG international standard for still image compression.

Nonlinear Dynamics of Trajectories Generated by Fully-Stretching Piecewise Linear Maps

2014 ◽  
Vol 24 (05) ◽  
pp. 1450071 ◽  
Author(s):  
T. Papamarkou ◽  
A. J. Lawrance
Keyword(s):  
Nonlinear Dynamics ◽  
Lyapunov Exponent ◽  
Piecewise Linear ◽  
Nonlinear Dynamical ◽  
Chaotic Orbits ◽  
Linear Maps ◽  
Piecewise Linear Maps ◽  
The Mean ◽  
Dynamical Properties ◽  
Analytical Expressions

This paper focuses on the nonlinear dynamical properties of chaotic orbits iteratively generated by maps composed of linear branches which expand across the whole map range. The nonlinear dynamics of such orbits involve both their statistical and chaotic properties. More specifically, analytical expressions are provided for the mean-adjusted quadratic autocorrelation function (ACF) and for the Lyapunov exponent of trajectories produced by the considered collection of piecewise linear maps.

Prediction of Solutions of the Duffing System with Tuned Mass Damper

2020 ◽  
Vol 22 (4) ◽  
pp. 983-990
Author(s):  
Konrad Mnich
Keyword(s):  
Dynamical System ◽  
Duffing Oscillator ◽  
Probabilistic Approach ◽  
Nonlinear Dynamical System ◽  
Tuned Mass Damper ◽  
Nonlinear Dynamical ◽  
Duffing System ◽  
Mass Damper ◽  
Basin Stability ◽  
Stability Concept

AbstractIn this work we analyze the behavior of a nonlinear dynamical system using a probabilistic approach. We focus on the coexistence of solutions and we check how the changes in the parameters of excitation influence the dynamics of the system. For the demonstration we use the Duffing oscillator with the tuned mass absorber. We mention the numerous attractors present in such a system and describe how they were found with the method based on the basin stability concept.

scholarly journals Robust Tracker of Hybrid Microgrids by the Invariant-Ellipsoid Set

Electronics ◽  
2021 ◽  
Vol 10 (15) ◽  
pp. 1794
Author(s):  
Hilmy Awad ◽  
Ehab H. E. Bayoumi ◽  
Hisham M. Soliman ◽  
Michele De Santis
Keyword(s):  
Sliding Mode ◽  
Tracking Error ◽  
Nonlinear Dynamical System ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Nonlinear Dynamical ◽  
Load Variations ◽  
Invariant Ellipsoid ◽  
Steady State Responses ◽  
Linearized Model

This paper introduces a new ellipsoidal-based tracker design to control a grid-connected hybrid direct current/alternating current (DC/AC) microgrid (MG). The proposed controller is robust against both parameters and load variations. The studied hybrid MG is modelled as a nonlinear dynamical system. A linearized model around an operating point is developed. The parameter changes are modelled as norm-bounded uncertainties. We apply the new extended version of the attractive (or invariant) ellipsoid for this tracking problem. Convex optimization is used to obtain the region’s minimal size where the tracking error between the state trajectories and the reference states converges. The sufficient conditions for stability are derived and solved based on linear matrix inequalities (LMIs). The proposed controller’s validity is shown via simulating the hybrid MG with various operational scenarios. In each scenario, the performance of the controller is compared with a recently proposed sliding mode controller. The comparison clearly illustrates the superiority of the developed controller in terms of transient and steady-state responses.

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