UMD Theses and Dissertations
Permanent URI for this collectionhttp://hdl.handle.net/1903/3
New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a given thesis/dissertation in DRUM.
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Item Energy absorption and diffusion in chaotic systems under rapid periodic driving(2022) Hodson, Wade Daniel; Jarzynski, Christopher; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this thesis, we study energy absorption in classical chaotic, ergodic systems subject to rapid periodic driving, and in related systems. Under a rapid periodic drive, we find that the energy evolution of chaotic systems appears as a random walk in energy space, which can be described as a process of energy diffusion. We characterize this process, and show that it generally predicts three stages of energy evolution: Initial relaxation to a prethermal state, followed by slow evolution of the system’s energy probability distribution in accordance with a Fokker-Planck equation, followed by either unbounded energy absorption or relaxation to an infinite temperature state. We then study the energy diffusion model in detail in driven billiard systems specifically; in particular, we obtain numerical results which corroborate the energy diffusion description for a specific choice of billiard. This is followed by an analysis of energy diffusion in one-dimensional oscillator systems subject to weak, correlated noise. Finally, we begin to investigate energy absorption in periodically driven quantum chaotic systems, i.e., quantum systems with a classical chaotic analogue. We invoke tools from Floquet theory and random matrix theory to investigate whether the classical energy diffusion framework can be applied to quantum systems, and under what conditions. We conclude with a discussion of potential models for energy absorption in quantum chaotic systems, and with an overview of open questions and directions for future work.Item Extensions of the Kuramoto model: from spiking neurons to swarming drones(2020) Chandra, Sarthak; Girvan, Michelle; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The Kuramoto model (KM) was initially proposed by Yoshiki Kuramoto in 1975 to model the dynamics of large populations of weakly coupled phase oscillators. Since then, the KM has proved to be a paradigmatic model, demonstrating dynamics that are complex enough to model a wide variety of nontrivial phenomena while remaining simple enough for detailed mathematical analyses. However, as a result of the mathematical simplifications in the construction of the model, the utility of the KM is somewhat restricted in its usual form. In this thesis we discuss extensions of the KM that allow it to be utilized in a wide variety of physical and biological problems. First, we discuss an extension of the KM that describes the dynamics of theta neurons, i.e., quadratic-integrate-and-fire neurons. In particular, we study networks of such neurons and derive a mean-field description of the collective neuronal dynamics and the effects of different network topologies on these dynamics. This mean-field description is achieved via an analytic dimensionality reduction of the network dynamics that allows for an efficient characterization of the system attractors and their dependence not only on the degree distribution but also on the degree correlations. Then, motivated by applications of the KM to the alignment of members in a two-dimensional swarm, we construct a Generalized Kuramoto Model (GKM) that extends the KM to arbitrary dimensions. Like the KM, the GKM in even dimensions continues to demonstrate a transition to coherence at a positive critical coupling strength. However, in odd dimensions the transition to coherence occurs discontinuously as the coupling strength is increased through 0. In contrast to the unique stable incoherent equilibrium for the KM, we find that for even dimensions larger than 2 the GKM displays a continuum of different possible pretransition incoherent equilibria, each with distinct stability properties, leading to a novel phenomenon, which we call `Instability-Mediated Resetting.' To aid the analysis of such systems, we construct an exact dimensionality reduction technique with applicability to not only the GKM, but also other similar systems with high-dimensional agents beyond the GKM.Item DYNAMICS OF LARGE SYSTEMS OF NONLINEARLY EVOLVING UNITS(2017) Lu, Zhixin; Ott, Edward; Chemical Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The dynamics of large systems of many nonlinearly evolving units is a general research area that has great importance for many areas in science and technology, including biology, computation by artificial neural networks, statistical mechanics, flocking in animal groups, the dynamics of coupled neurons in the brain, and many others. While universal principles and techniques are largely lacking in this broad area of research, there is still one particular phenomenon that seems to be broadly applicable. In particular, this is the idea of emergence, by which is meant macroscopic behaviors that “emerge” from a large system of many “smaller or simpler entities such that ... large entities” [i.e., macroscopic behaviors] arise which “exhibit properties the smaller/simpler entities do not exhibit.” [1]. In this thesis we investigate mechanisms and manifestations of emergence in four dynamical systems consisting many nonlinearly evolving units. These four systems are as follows. (a) We first study the motion of a large ensemble of many noninteracting particles in a slowly changing Hamiltonian system that undergoes a separatrix crossing. In such systems, we find that separatrix-crossing induces a counterintuitive effect. Specifically, numerical simulation of two sets of densely sprinkled initial conditions on two energy curves appears to suggest that the two energy curves, one originally enclosing the other, seemingly interchange their positions. This, however, is topologically forbidden. We resolve this paradox by introducing a numerical simulation method we call “robust” and study its consequences. (b) We next study the collective dynamics of oscillatory pacemaker neurons in Suprachiasmatic Nucleus (SCN), which, through synchrony, govern the circadian rhythm of mammals. We start from a high-dimensional description of the many coupled oscillatory neuronal units within the SCN. This description is based on a forced Kuramoto model. We then reduce the system dimensionality by using the Ott Antonsen Ansatz and obtain a low-dimensional macroscopic description. Using this reduced macroscopic system, we explain the east-west asymmetry of jet-lag recovery and discus the consequences of our findings. (c) Thirdly, we study neuron firing in integrate-and-fire neural networks. We build a discrete-state/discrete-time model with both excitatory and inhibitory neurons and find a phase transition between avalanching dynamics and ceaseless firing dynamics. Power-law firing avalanche size/duration distributions are observed at critical parameter values. Furthermore, in this critical regime we find the same power law exponents as those observed from experiments and previous, more restricted, simulation studies. We also employ a mean-field method and show that inhibitory neurons in this system promote robustness of the criticality (i.e., an enhanced range of system parameter where power-law avalanche statistics applies). (d) Lastly, we study the dynamics of “reservoir computing networks” (RCN’s), which is a recurrent neural network (RNN) scheme for machine learning. The ad- vantage of RCN’s over traditional RNN’s is that the training is done only on the output layer, usually via a simple least-square method. We show that RCN’s are very effective for inferring unmeasured state variables of dynamical systems whose system state is only partially measured. Using the examples of the Lorenz system and the Rossler system we demonstrate the potential of an RCN to perform as an universal model-free “observer”.Item Chaos and Community Attachment in Rural Low-Income Families: Influences on Parenting and Early Childhood Language and Behavior Problems(2016) Duncan, Aimee Claire Drouin; Harden, Brenda J; Human Development; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Families in rural poverty are vulnerable to a range of environmental stressors that negatively impact early childhood outcomes. There is a need for comprehensive research on the context of rural poverty and its impact on a variety of family and developmental processes. This research would inform the development of parenting and early childhood programs by providing information on the risks rural low-income families face, the resources they have, and the services they need to promote the best possible outcomes for vulnerable children and families. I intended to address the persistent gap in the empirical literature specific to family processes and child development in low-income, rural communities. My major goal was to enhance our understanding of the mechanisms which affect parenting within the context of rural poverty and their influence on child language and problem behaviors , specifically those related to school readiness. Participants were low-income rural parents (N = 97) and their preschool age children (M=42 months). Data were collected at one time point in the participants’ homes and included measures of chaos, community attachment, parenting stress, parenting, and child language and behaviors. Hierarchical regression and measured variable path analysis were used to test the relationships between variables. I found that chaos was significantly related to parenting stress. Community attachment was also found to be significantly related to parenting stress. In addition, positive parenting was significantly related to language outcomes but did not have a significant relationship with behavior problems. Finally, results from my study did not reveal a mediating role of parenting and parenting stress in the relationship between risk and protective factors and child language and behavior problems. My findings are considered in the context of the literature on rural low-income families, and of policy and practice.Item Complex dynamics of a microwave time-delayed feedback loop(2013) Dao, Hien Thi Le; Murphy, Thomas E; Rodgers, John C; Chemical Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The subject of this thesis is deterministic behaviors generated from a microwave time-delayed feedback loop. Time-delayed feedback systems are especially interesting because of the rich variety of dynamical behaviors that they can support. While ordinary differential equations must be of at least third-order to produce chaos, even a simple first-order nonlinear delay differential equation can produce higher-dimensional chaotic dynamics. The system reported in the thesis is governed by a very simple nonlinear delay differential equation. The experimental implementation uses both microwave and digital components to achieve the nonlinearity and time-delayed feedback, respectively. When a sinusoidal nonlinearity is incorporated, the dynamical behaviors range from fixed-point to periodic to chaotic depending on the feedback strength. The microwave frequency modulated chaotic signal generated by this system offers advantages in range and velocity sensing applications. When the sinusoidal nonlinearity is replaced by a binary nonlinearity, the system exhibits a complex periodic attractor with no fixed-point solution. Although there are many classic electronic circuits that produce chaotic behavior, microwave sources of chaos are especially relevant in communication and sensing applications where the signal must be transmitted between locations. The system also can exhibit random walk behavior when being operated in a higher feedback strength regime. Depending on the feedback strength values, the random behaviors can have properties of a regular or fractional Brownian motion. By unidirectional coupling two systems in the baseband, envelope synchronization between two deterministic Brownian motions can be achieved.Item Chaotic Oscillations in CMOS Integrated Circuits(2013) Park, Myunghwan; Lathrop, Daniel P; Rodgers, John C; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Chaos is a purely mathematical term, describing a signal that is aperiodic and sensitive to initial conditions, but deterministic. Yet, engineers usually see it as an undesirable effect to be avoided in electronics. The first part of the dissertation deals with chaotic oscillation in complementary metal-oxide-semiconductor integrated circuits (CMOS ICs) as an effect behavior due to high power microwave or directed electromagnetic energy source. When the circuit is exposed to external electromagnetic sources, it has long been conjectured that spurious oscillation is generated in the circuits. In the first part of this work, we experimentally and numerically demonstrate that these spurious oscillations, or out-of-band oscillations are in fact chaotic oscillations. In the second part of the thesis, we exploit a CMOS chaotic oscillator in building a cryptographic source, a random number generator. We first demonstrate the presence of chaotic oscillation in standard CMOS circuits. At radio frequencies, ordinary digital circuits can show unexpected nonlinear responses. We evaluate a CMOS inverter coupled with electrostatic discharging (ESD) protection circuits, designed with 0.5 μm CMOS technology, for their chaotic oscillations. As the circuit is driven by a direct radio frequency injection, it exhibits a chaotic dynamics, when the input frequency is higher than the typical maximum operating frequency of the CMOS inverter. We observe an aperiodic signal, a broadband spectrum, and various bifurcations in the experimental results. We analytically discuss the nonlinear physical effects in the given circuit : ESD diode rectification, DC bias shift due to a non-quasi static regime operation of the ESD PN-junction diode, and a nonlinear resonant feedback current path. In order to predict these chaotic dynamics, we use a transistor-based model, and compare the model's performance with the experimental results. In order to verify the presence of chaotic oscillations mathematically, we build on an ordinary differential equation model with the circuit-related nonlinearities. We then calculate the largest Lyapunov exponents to verify the chaotic dynamics. The importance of this work lies in investigating chaotic dynamics of standard CMOS ICs that has long been conjectured. In doing so, we experimentally and numerically give evidences for the presence of chaotic oscillations. We then report on a random number generator design, in which randomness derives from a Boolean chaotic oscillator, designed and fabricated as an integrated circuit. The underlying physics of the chaotic dynamics in the Boolean chaotic oscillator is given by the Boolean delay equation. According to numerical analysis of the Boolean delay equation, a single node network generates chaotic oscillations when two delay inputs are incommensurate numbers and the transition time is fast. To test this hypothesis physically, a discrete Boolean chaotic oscillator is implemented. Using a CMOS 0.5 μm process, we design and fabricate a CMOS Boolean chaotic oscillator which consists of a core chaotic oscillator and a source follower buffer. Chaotic dynamics are verified using time and frequency domain analysis, and the largest Lyapunov exponents are calculated. The measured bit sequences do make a suitable randomness source, as determined via National Institute of Standards and Technology (NIST) standard statistical tests version 2.1.Item Synchronization of Chaotic Optoelectronic Oscillators: Adaptive Techniques and the Design of Optimal Networks(2011) Ravoori, Bhargava; Roy, Rajarshi; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Synchronization in networks of chaotic systems is an interesting phenomenon with potential applications to sensing, parameter estimation and communications. Synchronization of chaos, in addition to being influenced by the dynamical nature of the constituent network units, is critically dependent upon the maintenance of a proper coupling between the systems. In practical situations, however, synchronization in chaotic networks is negatively affected by perturbations in the coupling channels. Here, using a fiber-optic network of chaotic optoelectronic oscillators, we experimentally demonstrate an adaptive algorithm that maintains global network synchrony even when the coupling strengths are unknown and time-varying. Our adaptive algorithm operates by generating real-time estimates of the coupling perturbations which are subsequently used to suitably adjust internal node parameters in order to compensate for external disturbances. In our work, we also examine the influence of network configuration on synchronization. Through measurements of the convergence rate to synchronization in networks of optoelectronic systems, we show that having more network links does not necessarily imply faster or better synchronization as is generally thought. We find that the convergence rate is maximized for certain network configurations, called optimal networks, which are identified based on the eigenvalues of the coupling matrix. Further, based on an analysis of the eigenvectors of the coupling matrix, we introduce a classification system that categorizes networks according to their sensitivity to coupling perturbations as sensitive and nonsensitive configurations. Though our experiments are performed on networks consisting of specific nonlinear optoelectronic oscillators, the theoretical basis of our studies is general and consequently many of our results are applicable to networks of arbitrary dynamical oscillators.Item Making Forecasts for Chaotic Processes in the Presence of Model Error(2006-02-20) Danforth, Christopher M; Yorke, James A; Kalnay, Eugenia; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Numerical weather forecast errors are generated by model deficiencies and by errors in the initial conditions which interact and grow nonlinearly. With recent progress in data assimilation, the accuracy in the initial conditions has been substantially improved so that accounting for systematic errors associated with model deficiencies has become even more important to ensemble prediction and data assimilation applications. This dissertation describes two new methods for reducing the effect of model error in forecasts. The first method is inspired by Leith (1978) who proposed a statistical method to account for model bias and systematic errors linearly dependent on the flow anomalies. DelSole and Hou (1999) showed this method to be successful when applied to a very low order quasi-geostrophic model simulation with artificial "model errors." However, Leith's method is computationally prohibitive for high-resolution operational models. The purpose of the present study is to explore the feasibility of estimating and correcting systematic model errors using a simple and efficient procedure that could be applied operationally, and to compare the impact of correcting the model integration with statistical corrections performed a posteriori. The second method is inspired by the dynamical systems theory of shadowing. Making a prediction for a chaotic physical process involves specifying the probability associated with each possible outcome. Ensembles of solutions are frequently used to estimate this probability distribution. However, for a typical chaotic physical system H and model L of that system, no solution of L remains close to H for all time. We propose an alternative and show how to "inflate" or systematically perturb the ensemble of solutions of L so that some ensemble member remains close to H for orders of magnitude longer than unperturbed solutions of L. This is true even when the perturbations are significantly smaller than the model error.Item Finding Optimal Orbits of Chaotic Systems(2005-12-05) Grant, Angela Elyse; Hunt, Brian R; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Chaotic dynamical systems can exhibit a wide variety of motions, including periodic orbits of arbitrarily large period. We consider the question of which motion is optimal, in the sense that it maximizes the average over time of some given scalar ``performance function." Past work indicates that optimal motions tend to be periodic orbits with low period, but does not describe, beyond a brute force approach, how to determine which orbit is optimal in a particular scenario. For one-dimensional expanding maps and higher dimensional hyperbolic systems, we have found constructive methods for calculating the optimal average and corresponding periodic orbit, and by carrying them out on a computer have found them to work quite well in practice.Item Application of Chaotic Synchronization and Controlling Chaos to Communications(2005-04-19) Dronov, Vasily; Ott, Edward; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This thesis addresses two important issues that are applicable to chaotic communication systems: synchronization of chaos and controlling chaos. Synchronization of chaos is a naturally occurring phenomenon where one chaotic dynamical system mimics dynamical behavior of another chaotic system. The phenomenon of chaotic synchronization is a popular topic of research, in general, and has attracted much attention within the scientific community. Controlling chaos is another potential engineering application. A unique property of controlling chaos is the ability to cause large long-term impact on the dynamics using arbitrarily small perturbations. This thesis is broken up into three chapters. The first chapter contains a brief introduction to the areas of research of the thesis work, as well as the summaries the work itself. The second chapter is dedicated to the study of a particular situation of chaotic synchronization which leads to a novel structure of the basin of attraction. This chapter also develops theoretical scalings applicable to these systems and compares results of our numerical simulations on three different chaotic systems. The third chapter consists or two logically connected parts (both of them study chaotic systems that can be modeled with delayed differential equations). The first and the main part presents a study of a chaotically behaving traveling wave tube, or TWT, with the objective of improving efficiency of satellite communication systems. In this work we go through an almost complete design cycle, where, given an objective, we begin with developing a nonlinear model for a generic TWT; we then study numerically the dynamics of the proposed model; we find conditions where chaotic behavior occurs (we argue that TWT in chaotic mode could be more power efficient); then we use the idea of controlling chaos for information encoding; we support the concept with numerical simulations; and finally analyze the performance of the proposed chaotic communication system. The second part of this chapter describes an experiment with a pair of electronic circuits modeling the well-known Mackey-Glass equation. An experiment where human voice was encoded into chaotic signal had been conducted which showed a possibility of engineering application of chaos to secure communications.