scholarly journals Dynamical system decomposition using dissipation inequalities

2011 ◽  
Author(s):  
James Anderson ◽  
Andre Teixeira ◽  
Henrik Sandberg ◽  
Antonis Papachristodoulou
Keyword(s):  
Dynamical System ◽  
System Decomposition ◽  
Dissipation Inequalities

scholarly journals Potential Function in a Continuous Dissipative Chaotic System: Decomposition Scheme and Role of Strange Attractor

2014 ◽  
Vol 24 (02) ◽  
pp. 1450015 ◽  
Author(s):  
Yian Ma ◽  
Qijun Tan ◽  
Ruoshi Yuan ◽  
Bo Yuan ◽  
Ping Ao
Keyword(s):  
Dynamical System ◽  
Potential Function ◽  
Chaotic System ◽  
Strange Attractor ◽  
Deterministic System ◽  
System Decomposition ◽  
Decomposition Scheme ◽  
Dynamical Properties ◽  
Different Origins

We demonstrate, first in literature, that potential functions can be constructed in a continuous dissipative chaotic system and can be used to reveal its dynamical properties. To attain this aim, a Lorenz-like system is proposed and rigorously proved chaotic for exemplified analysis. We explicitly construct a potential function monotonically decreasing along the system's dynamics, revealing the structure of the chaotic strange attractor. The potential function is not unique for a deterministic system. We also decompose the dynamical system corresponding to a curl-free structure and a divergence-free structure, explaining for the different origins of chaotic attractor and strange attractor. Consequently, reasons for the existence of both chaotic nonstrange attractors and nonchaotic strange attractors are discussed within current decomposition framework.

On the Harmonic Oscillations for the Motion of a Dynamical System

2017 ◽  
Vol 13 (2) ◽  
pp. 4657-4670
Author(s):  
W. S. Amer
Keyword(s):  
Dynamical System ◽  
Numerical Solutions ◽  
Equation Of Motion ◽  
Parameter Method ◽  
Kutta Method ◽  
Small Parameter Method ◽  
Harmonic Oscillations ◽  
Pivot Point ◽  
Runge Kutta Method ◽  
High Consistency

This work touches two important cases for the motion of a pendulum called Sub and Ultra-harmonic cases. The small parameter method is used to obtain the approximate analytic periodic solutions of the equation of motion when the pivot point of the pendulum moves in an elliptic path. Moreover, the fourth order Runge-Kutta method is used to investigate the numerical solutions of the considered model. The comparison between both the analytical solution and the numerical ones shows high consistency between them.

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