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Full-Text Articles in Non-linear Dynamics
A Novel Method For Sensitivity Analysis Of Time-Averaged Chaotic System Solutions, Christian A. Spencer-Coker
A Novel Method For Sensitivity Analysis Of Time-Averaged Chaotic System Solutions, Christian A. Spencer-Coker
Theses and Dissertations
The direct and adjoint methods are to linearize the time-averaged solution of bounded dynamical systems about one or more design parameters. Hence, such methods are one way to obtain the gradient necessary in locally optimizing a dynamical system’s time-averaged behavior over those design parameters. However, when analyzing nonlinear systems whose solutions exhibit chaos, standard direct and adjoint sensitivity methods yield meaningless results due to time-local instability of the system. The present work proposes a new method of solving the direct and adjoint linear systems in time, then tests that method’s ability to solve instances of the Lorenz system that exhibit …
Dynamic Parameter Estimation From Partial Observations Of The Lorenz System, Eunice Ng
Dynamic Parameter Estimation From Partial Observations Of The Lorenz System, Eunice Ng
Theses and Dissertations
Recent numerical work of Carlson-Hudson-Larios leverages a nudging-based algorithm for data assimilation to asymptotically recover viscosity in the 2D Navier-Stokes equations as partial observations on the velocity are received continuously-in-time. This "on-the-fly" algorithm is studied both analytically and numerically for the Lorenz equations in this thesis.
Practical Chaos: Using Dynamical Systems To Encrypt Audio And Visual Data, Julia Ruiter
Practical Chaos: Using Dynamical Systems To Encrypt Audio And Visual Data, Julia Ruiter
Scripps Senior Theses
Although dynamical systems have a multitude of classical uses in physics and applied mathematics, new research in theoretical computer science shows that dynamical systems can also be used as a highly secure method of encrypting data. Properties of Lorenz and similar systems of equations yield chaotic outputs that are good at masking the underlying data both physically and mathematically. This paper aims to show how Lorenz systems may be used to encrypt text and image data, as well as provide a framework for how physical mechanisms may be built using these properties to transmit encrypted wave signals.
Investigation Of Chaos In Biological Systems, Navaneeth Mohan
Investigation Of Chaos In Biological Systems, Navaneeth Mohan
Electronic Thesis and Dissertation Repository
Chaos is the seemingly irregular behavior arising from a deterministic system. Chaos is observed in many real-world systems. Edward Lorenz’s seminal discovery of chaotic behavior in a weather model has prompted researchers to develop tools that distinguish chaos from non-chaotic behavior. In the first chapter of this thesis, I survey the tools for detecting chaos namely, Poincaré maps, Lyapunov exponents, surrogate data analysis, recurrence plots and correlation integral plots. In chapter two, I investigate blood pressure fluctuations for chaotic signatures. Though my analysis reveals interesting evidence in support of chaos, the utility such an analysis lies in a different direction …