Dynamical Systems: Chaotic Attractors and Synchronization using Time-Averaged Partial Observations of the Phase Space
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Authors
Blocher, Jordan
Issue Date
2016
Type
Thesis
Language
Keywords
Chaotic Attractor , Dissipative , Feedback Control , Lorenz , Stochastic Noise , Synchronization
Alternative Title
Abstract
We study the synchronization of chaotic systems when the coupling between themcontains both time averages and stochastic noise. Our model dynamics are givenby the Lorenz equations which are a system of three ordinary differential equationsin the variables X, Y and Z. Our theoretical results show that coupling two copiesof the Lorenz equations using a feedback control which consists of time averages ofthe X variable leads to exact synchronization provided the time-averaging windowis known and sufficiently small. In the presence of noise the convergence is towithin a factor of the variance of the noise. The novelty of our investigationhinges on the analysis of the time averages. We also consider the case whenthe time-averaging window is not known and show that it is possible to tunethe feedback control to recover the size of the time-averaging window. Furthernumerical computations show that synchronization is more accurate and occursunder much less stringent conditions than our theory requires.
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In Copyright(All Rights Reserved)