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(1 - 11 of 11)
- Title
- A proposal for a binary stream cipher based on chaos theory.
- Creator
- Kanser, Heather Lianna, Florida Atlantic University, Mullin, Ronald C., Hoffman, Frederick, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
Today new secure cryptosystems are in great demand. Computers are becoming more powerful and old cryptosystems, such as the Data Encryption Standard (DES), are becoming outdated. This thesis describes a new binary additive strewn cipher (HK cryptosystem) that is based on the logistic map. The logistic map is not random, but works under simple rules to become complex, thus making it ideal for implementation in cryptography. Instead of basing the algorithm on one logistic map, the HK...
Show moreToday new secure cryptosystems are in great demand. Computers are becoming more powerful and old cryptosystems, such as the Data Encryption Standard (DES), are becoming outdated. This thesis describes a new binary additive strewn cipher (HK cryptosystem) that is based on the logistic map. The logistic map is not random, but works under simple rules to become complex, thus making it ideal for implementation in cryptography. Instead of basing the algorithm on one logistic map, the HK cryptosystem. averages several uncoupled logistic maps. Averaging the maps increases the dimension of such a system, thus providing greater security. This thesis will explore the strengths and weaknesses of the HK cryptosystem and will end by introducing a modified version, called the HK8 cryptosystem that does not have the apparent weakness of the HK system.
Show less - Date Issued
- 2000
- PURL
- http://purl.flvc.org/fcla/dt/12685
- Subject Headings
- Chaotic behavior in systems, Computers--Access control, Cryptography
- Format
- Document (PDF)
- Title
- Output Stability Analysis for Nonlinear Systems with Time Delays.
- Creator
- Gallolu Kankanamalage, Hasala Senpathy, Wang, Yuan, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
Systems with time delays have a broad range of applications not only in control systems but also in many other disciplines such as mathematical biology, financial economics, etc. The time delays cause more complex behaviours of the systems. It requires more sophisticated analysis due to the infinite dimensional structure of the space spaces. In this thesis we investigate stability properties associated with output functions of delay systems. Our primary target is the equivalent Lyapunov...
Show moreSystems with time delays have a broad range of applications not only in control systems but also in many other disciplines such as mathematical biology, financial economics, etc. The time delays cause more complex behaviours of the systems. It requires more sophisticated analysis due to the infinite dimensional structure of the space spaces. In this thesis we investigate stability properties associated with output functions of delay systems. Our primary target is the equivalent Lyapunov characterization of input-tooutput stability (ios). A main approach used in this work is the Lyapuno Krasovskii functional method. The Lyapunov characterization of the so called output-Lagrange stability is technically the backbone of this work, as it induces a Lyapunov description for all the other output stability properties, in particular for ios. In the study, we consider two types of output functions. The first type is defined in between Banach spaces, whereas the second type is defined between Euclidean spaces. The Lyapunov characterization for the first type of output maps provides equivalence between the stability properties and the existence of the Lyapunov-Krasovskii functionals. On the other hand, as a special case of the first type, the second type output renders flexible Lyapunov descriptions that are more efficient in applications. In the special case when the output variables represent the complete collection of the state variables, our Lyapunov work lead to Lyapunov characterizations of iss, complementing the current iss theory with some novel results. We also aim at understanding how output stability are affected by the initial data and the external signals. Since the output variables are in general not a full collection of the state variables, the overshoots and decay properties may be affected in different ways by the initial data of either the state variables or just only the output variables. Accordingly, there are different ways of defining notions on output stability, making them mathematically precisely. After presenting the definitions, we explore the connections of these notions. Understanding the relation among the notions is not only mathematically necessary, it also provides guidelines in system control and design.
Show less - Date Issued
- 2017
- PURL
- http://purl.flvc.org/fau/fd/FA00004935, http://purl.flvc.org/fau/fd/FA00004935
- Subject Headings
- Nonlinear systems., Time delay systems., Multiagent systems., Adaptive control systems., Chaotic behavior in systems.
- Format
- Document (PDF)
- Title
- Two lessons from fractals and chaos.
- Creator
- Liebovitch, Larry S., Scheurle, Daniela
- Date Issued
- 2000
- PURL
- http://purl.flvc.org/fau/165936
- Subject Headings
- Fractals, Nonlinear systems, Mathematical models, Chaos, Chaotic behavior in systems, Biomathematics
- Format
- Document (PDF)
- Title
- Derivation of planar diffeomorphisms from Hamiltonians with a kick.
- Creator
- Barney, Zalmond C., Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
In this thesis we will discuss connections between Hamiltonian systems with a periodic kick and planar diffeomorphisms. After a brief overview of Hamiltonian theory we will focus, as an example, on derivations of the Hâenon map that can be obtained by considering kicked Hamiltonian systems. We will conclude with examples of Hâenon maps of interest.
- Date Issued
- 2011
- PURL
- http://purl.flvc.org/FAU/3329833
- Subject Headings
- Mathematical physics, Differential equations, Partial, Hamiltonian systems, Algebra, Linear, Chaotic behavior in systems
- Format
- Document (PDF)
- Title
- Introduction to fractals.
- Creator
- Liebovitch, Larry S., Shehadeh, Lina A.
- PURL
- http://purl.flvc.org/fau/165810
- Subject Headings
- Fractals, Chaotic behavior in systems, Nonlinear systems--Mathematical models, Ion channels, Psychology
- Format
- Document (PDF)
- Title
- SUSTAINING CHAOS USING DEEP REINFORCEMENT LEARNING.
- Creator
- Vashishtha, Sumit, Verma, Siddhartha, Florida Atlantic University, Department of Ocean and Mechanical Engineering, College of Engineering and Computer Science
- Abstract/Description
-
Numerous examples arise in fields ranging from mechanics to biology where disappearance of Chaos can be detrimental. Preventing such transient nature of chaos has been proven to be quite challenging. The utility of Reinforcement Learning (RL), which is a specific class of machine learning techniques, in discovering effective control mechanisms in this regard is shown. The autonomous control algorithm is able to prevent the disappearance of chaos in the Lorenz system exhibiting meta-stable...
Show moreNumerous examples arise in fields ranging from mechanics to biology where disappearance of Chaos can be detrimental. Preventing such transient nature of chaos has been proven to be quite challenging. The utility of Reinforcement Learning (RL), which is a specific class of machine learning techniques, in discovering effective control mechanisms in this regard is shown. The autonomous control algorithm is able to prevent the disappearance of chaos in the Lorenz system exhibiting meta-stable chaos, without requiring any a-priori knowledge about the underlying dynamics. The autonomous decisions taken by the RL algorithm are analyzed to understand how the system’s dynamics are impacted. Learning from this analysis, a simple control-law capable of restoring chaotic behavior is formulated. The reverse-engineering approach adopted in this work underlines the immense potential of the techniques used here to discover effective control strategies in complex dynamical systems. The autonomous nature of the learning algorithm makes it applicable to a diverse variety of non-linear systems, and highlights the potential of RLenabled control for regulating other transient-chaos like catastrophic events.
Show less - Date Issued
- 2020
- PURL
- http://purl.flvc.org/fau/fd/FA00013498
- Subject Headings
- Machine learning--Technique, Reinforcement learning, Algorithms, Chaotic behavior in systems, Nonlinear systems
- Format
- Document (PDF)
- Title
- Nonlinear resonance: determining maximal autoresonant response and modulation of spontaneous otoacoustic emissions.
- Creator
- Witkov, Carey., Charles E. Schmidt College of Science, Center for Complex Systems and Brain Sciences
- Abstract/Description
-
Sustained resonance in a linear oscillator is achievable with a drive whose constant frequency matches the resonant frequency of the oscillator. In oscillators with nonlinear restoring forces, i.e., Dung-type oscillators, resonant frequency changes with amplitude, so a constant frequency drive generates a beat oscillation instead of sustained resonance. Dung-type oscillators can be driven into sustained resonance, called autoresonance (AR), when drive frequency is swept in time to match the...
Show moreSustained resonance in a linear oscillator is achievable with a drive whose constant frequency matches the resonant frequency of the oscillator. In oscillators with nonlinear restoring forces, i.e., Dung-type oscillators, resonant frequency changes with amplitude, so a constant frequency drive generates a beat oscillation instead of sustained resonance. Dung-type oscillators can be driven into sustained resonance, called autoresonance (AR), when drive frequency is swept in time to match the changing resonant frequency of the oscillator. It is found that near-optimal drive linear sweep rates for autoresonance can be estimated from the beat oscillation resulting from constant frequency excitation. Specically, a least squares estimate of the slope of the Teager-Kaiser instantaneous frequency versus time plot for the rising half-cycle of the beat response to a stationary drive provides a near-optimal estimate of the linear drive sweep rate that sustains resonance in the pendulum, Dung and Dung-Van der Pol oscillators. These predictions are confirmed with model-based numerical simulations. A closed-form approximation to the AM-FM nonlinear resonance beat response of a Dung oscillator driven at its low-amplitude oscillator frequency is obtained from a solution to an associated Mathieu equation. AR time responses are found to evolve along a Mathieu equation primary resonance stability boundary. AR breakdown occurs at sweep rates just past optimal and map to a single stable point just off the Mathieu equation primary resonance stability boundary. Optimal AR sweep rates produce oscillating phase dierences with extrema near 90 degrees, allowing extended time in resonance. AR breakdown occurs when phase difference equals 180 degrees. Nonlinear resonance of the van der Pol type may play a role in the extraordinary sensitivity of the human ear., The mechanism for maintaining the cochlear amplifier at its critical point is currently unknown. The possibility of open-loop control of cochlear operating point, maintaining criticality on average through periodically varying damping (super-regeneration) motivates a study of spontaneous otoacoustic emission (SOAE) amplitude modulation on a short (msec) time scale. An example of periodic amplitude modulation within a wide filter bandwidth is found that appears to be a beat oscillation of two SOAEs.
Show less - Date Issued
- 2011
- PURL
- http://purl.flvc.org/FAU/3174314
- Subject Headings
- Otoacoustic emissions, Chaotic behavior in systems, Nonlinear theories, Pattern recognition systems
- Format
- Document (PDF)
- Title
- Fractal methods to analyze ion channel kinetics.
- Creator
- Liebovitch, Larry S., Scheurle, Daniela, Rusek, Marian, Zochowskis, Michal
- Date Issued
- 2001-08
- PURL
- http://purl.flvc.org/FAU/165246
- Subject Headings
- Fractals, Ion Channels-Mathematical models, Ion flow dynamics, Biomathematics, Chaotic behavior in systems
- Format
- Document (PDF)
- Title
- Nonlinear Phenomena from a Reinjected Horseshoe.
- Creator
- Fontaine, Marcus, Kalies, William D., Naudot, Vincent, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
A geometric model of a reinjected cuspidal horseshoe is constructed, that resembles the standard horseshoe, but where the set of points that escape are now reinjected and contribute to richer dynamics. We show it is observed in the unfolding of a three-dimensional vector field possessing an inclination-flip homoclinic orbit with a resonant hyperbolic equilibrium. We use techniques from classical dynamical systems theory and rigorous computational symbolic dynamics with algebraic topology to...
Show moreA geometric model of a reinjected cuspidal horseshoe is constructed, that resembles the standard horseshoe, but where the set of points that escape are now reinjected and contribute to richer dynamics. We show it is observed in the unfolding of a three-dimensional vector field possessing an inclination-flip homoclinic orbit with a resonant hyperbolic equilibrium. We use techniques from classical dynamical systems theory and rigorous computational symbolic dynamics with algebraic topology to show that for suitable parameters the flow contains a strange attractor.
Show less - Date Issued
- 2016
- PURL
- http://purl.flvc.org/fau/fd/FA00004591
- Subject Headings
- Nonlinear theories., Computational dynamics., Attractors (Mathematics), Chaotic behavior in systems., Mathematical physics.
- Format
- Document (PDF)
- Title
- Time series analysis and correlation dimension estimation: Mathematical foundation and applications.
- Creator
- Jiang, Wangye, Florida Atlantic University, Ding, Mingzhou, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
A time series is a data set of a single quantity sampled at intervals T time units apart. It is widely used to represent a chaotic dynamical system. The correlation dimension measures the complexity of a dynamical system. Using the delay-coordinate map and the extended GP algorithm one can estimate the correlation dimension of an experimental dynamical system from measured time series. This thesis discusses the mathematical foundation of the methods and the corresponding applications. The...
Show moreA time series is a data set of a single quantity sampled at intervals T time units apart. It is widely used to represent a chaotic dynamical system. The correlation dimension measures the complexity of a dynamical system. Using the delay-coordinate map and the extended GP algorithm one can estimate the correlation dimension of an experimental dynamical system from measured time series. This thesis discusses the mathematical foundation of the methods and the corresponding applications. The embedding theorems and their relationship with dimension preservation are reviewed in detail, but more attention is focussed on the concept development.
Show less - Date Issued
- 1995
- PURL
- http://purl.flvc.org/fcla/dt/15213
- Subject Headings
- Time-series analysis--Mathematical models, Chaotic behavior in systems
- Format
- Document (PDF)
- Title
- Self-organizing dynamics of coupled map systems.
- Creator
- Liebovitch, Larry S., Zochowski, Michal
- Date Issued
- 1999-03
- PURL
- http://purl.flvc.org/fau/165481
- Subject Headings
- Dynamics--Mathematical models, Chaotic behavior in systems, Self-organizing maps, Self-organizing systems-Mathematical models
- Format
- Document (PDF)
