Localizing the Chaotic Strange Attractors of Multiparameter Nonlinear Dynamical Systems using Competitive Modes A Literary Analysis Table of Contents Introduction Strange Attractors and Chaos Localization through Competitive Modes Lorenz
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Presentation Transcript
01
Localizing the Chaotic Strange Attractors of Multiparameter Nonlinear Dynamical Systems using Competitive Modes A Literary Analysis<br>
02
Table of Contents Introduction
Strange Attractors and Chaos
Localization through Competitive Modes
Lorenz Attractor Example
Conclusions<br>
03
Dynamical Systems Introduction
Strange Attractors
Competitive Modes
Conclusions<br>
04
Strange Attractors Definition: The strange attractor A of a n-dimensional system of differential equations is an attractor that is fractal in nature. Introduction
Strange Attractors
Competitive Modes
Conclusions<br>
05
Chaos Introduction
Strange Attractors
Competitive Modes
Conclusions<br>
06
Chaos: Lorenz Introduction
Strange Attractors
Competitive Modes
Conclusions<br>
07
Localization
Through
Competitive Modes<br>
08
Oscillators Introduction
Strange Attractors
Competitive Modes
Conclusions<br>
09
Oscillators Introduction
Strange Attractors
Competitive Modes
Conclusions<br>
10
Oscillators to Competitive Modes Introduction
Strange Attractors
Competitive Modes
Conclusions<br>
11
Oscillators to Competitive Modes Introduction
Strange Attractors
Competitive Modes
Conclusions<br>
12
Competitive Mode Conjecture Introduction
Strange Attractors
Competitive Modes
Conclusions<br>
13
Competitive Modes: Lorenz Introduction
Strange Attractors
Competitive Modes
Conclusions<br>
14
Competitive Modes: Lorenz Introduction
Strange Attractors
Competitive Modes
Conclusions<br>
15
Competitive Modes: Lorenz Introduction
Strange Attractors
Competitive Modes
Conclusions<br>
16
Conclusions and Research Questions Localization techniques do already exist, but are not necessarily simple.
Is the Competitive Mode Conjecture true?
Which systems fulfill the competitive mode conjecture?
Does it also apply to discrete systems? Introduction
Strange Attractors
Competitive Modes
Conclusions<br>
17
Questions? Introduction
Strange Attractors
Competitive Modes
Conclusions<br>
18
Localization through Trajectories Introduction
Strange Attractors
Trajectories
Nambu Mechanics
Competitive Modes
Conclusions<br>
19
Localization through Trajectories Self-Excited Attractors
Hidden Attractors Introduction
Strange Attractors
Trajectories
Nambu Mechanics
Competitive Modes
Conclusions<br>
20
Localization of Chua Hidden Attractor Introduction
Strange Attractors
Trajectories
Nambu Mechanics
Competitive Modes
Conclusions<br>
21
Localization of Chua Hidden Attractor Introduction
Strange Attractors
Trajectories
Nambu Mechanics
Competitive Modes
Conclusions<br>
22
Localization of Chua Hidden Attractor Introduction
