# Dynamical Systems Commons™

Articles 1 - 30 of 295

## Full-Text Articles in Dynamical Systems

Jun 2020

#### Symmetric Rigidity For Circle Endomorphisms With Bounded Geometry And Their Dual Maps, John Adamski

##### All Dissertations, Theses, and Capstone Projects

Let $f$ be a circle endomorphism of degree $d\geq2$ that generates a sequence of Markov partitions that either has bounded nearby geometry and bounded geometry, or else just has bounded geometry, with respect to normalized Lebesgue measure. We define the dual symbolic space $\S^*$ and the dual circle endomorphism $f^*=\tilde{h}\circ f\circ{h}^{-1}$, which is topologically conjugate to $f$. We describe some properties of the topological conjugacy $\tilde{h}$. We also describe an algorithm for generating arbitrary circle endomorphisms $f$ with bounded geometry that preserve Lebesgue measure and their corresponding dual circle endomorphisms $f^*$ as ...

Oscillations Via Excitable Cells, Derek Orr, Bard Ermentrout May 2020

#### Oscillations Via Excitable Cells, Derek Orr, Bard Ermentrout

##### Biology and Medicine Through Mathematics Conference

No abstract provided.

Modeling Vaccination Strategies To Control White-Nose Syndrome In Little Brown Bat Colonies, Eva Cornwell, David Elzinga, Shelby R. Stowe, Alex Capaldi May 2020

#### Modeling Vaccination Strategies To Control White-Nose Syndrome In Little Brown Bat Colonies, Eva Cornwell, David Elzinga, Shelby R. Stowe, Alex Capaldi

##### Biology and Medicine Through Mathematics Conference

No abstract provided.

Emergence, Mechanics, And Development: How Behavior And Geometry Underlie Cowrie Seashell Form, Michael G. Levy, Michael R. Deweese May 2020

#### Emergence, Mechanics, And Development: How Behavior And Geometry Underlie Cowrie Seashell Form, Michael G. Levy, Michael R. Deweese

##### Biology and Medicine Through Mathematics Conference

No abstract provided.

Nonlocal Helmholtz Decompositions And Connections To Classical Counterparts, Andrew Haar, Petronela Radu May 2020

#### Nonlocal Helmholtz Decompositions And Connections To Classical Counterparts, Andrew Haar, Petronela Radu

##### UCARE Research Products

In recent years nonlocal models have been successfully introduced in a variety of applications, such as dynamic fracture, nonlocal diffusion, flocking, and image processing. Thus, the development of a nonlocal calculus theory, together with the study of nonlocal operators has become the focus of many theoretical investigations. Our work focuses on a Helmholtz decomposition in the nonlocal (integral) framework. In the classical (differential) setting the Helmholtz decomposition states that we can decompose a three dimensional vector field as a sum of an irrotational function and a solenoidal function. We will define new nonlocal gradient and curl operators that allow us ...

The Game Of Life On The Hyperbolic Plane, Yuncong Gu May 2020

#### The Game Of Life On The Hyperbolic Plane, Yuncong Gu

##### Mathematical Sciences Technical Reports (MSTR)

In this paper, we work on the Game of Life on the hyperbolic plane. We are interested in different tessellations on the hyperbolic plane and different Game of Life rules. First, we show the exponential growth of polygons on the pentagon tessellation. Moreover, we find that the Group of 3 can keep the boundary of a set not getting smaller. We generalize the existence of still lifes by computer simulations. Also, we will prove some propositions of still lifes and cycles. There exists a still life under rules B1, B2, and S3.

Quantitative Analysis Of A Stochastic Seitr Epidemic Model With Multiple Stages Of Infection And Treatment, Olusegun M. Otunuga, Mobolaji O. Ogunsolu Jan 2020

#### Quantitative Analysis Of A Stochastic Seitr Epidemic Model With Multiple Stages Of Infection And Treatment, Olusegun M. Otunuga, Mobolaji O. Ogunsolu

##### Mathematics Faculty Research

We present a mathematical analysis of the transmission of certain diseases using a stochastic susceptible-exposed-infectious-treated-recovered (SEITR) model with multiple stages of infection and treatment and explore the effects of treatments and external ﬂuctuations in the transmission, treatment and recovery rates. We assume external ﬂuctuations are caused by variability in the number of contacts between infected and susceptible individuals. It is shown that the expected number of secondary infections produced (in the absence of noise) reduces as treatment is introduced into the population. By deﬁning RT,n and ℛT,n as the basic deterministic and stochastic reproduction numbers, respectively ...

#### Classifying Flow-Kick Equilibria: Reactivity And Transient Behavior In The Variational Equation, Alanna Haslam

##### Honors Projects

In light of concerns about climate change, there is interest in how sustainable management can maintain the resilience of ecosystems. We use flow-kick dynamical systems to model ecosystems subject to a constant kick occurring every τ time units. We classify the stability of flow-kick equilibria to determine which management strategies result in desirable long-term characteristics. To classify the stability of a flow-kick equilibrium, we classify the linearization of the time-τ map given by the time-τ map of the variational equation about the equilibrium trajectory. Since the variational equation is a non-autonomous linear differential equation, we conjecture that the asymptotic stability ...

Real-Time Monitoring Of Area Angles With Synchrophasor Measurements, Wenyun Ju, Ian Dobson, Kenneth Martin, Kai Sun, Neeraj Nayak, Iknoor Singh, Horacio Silva-Saravia, Anthony Faris, Lin Zhang, Yajun Wang Jan 2020

#### Real-Time Monitoring Of Area Angles With Synchrophasor Measurements, Wenyun Ju, Ian Dobson, Kenneth Martin, Kai Sun, Neeraj Nayak, Iknoor Singh, Horacio Silva-Saravia, Anthony Faris, Lin Zhang, Yajun Wang

##### Electrical and Computer Engineering Publications

This paper develops a comprehensive framework of Area Angle Monitoring (AAM) to monitor the stress of bulk power transfer across an area of a power transmission system in real-time. Area angle is calculated from synchrophasor measurements to provide alert to system operators if the area angle exceeds pre-defined thresholds. This paper proposes general methods to identify these warning and emergency thresholds, and tests a mitigation strategy to relieve the area stress when the area angle exceeds the threshold. In order to handle the limited coverage of synchrophasor measurements, this paper proposes methods to estimate phase angles for boundary buses without ...

Dec 2019

#### Theory Of Lexicographic Differentiation In The Banach Space Setting, Jaeho Choi

##### Electronic Theses and Dissertations

Derivative information is useful for many problems found in science and engineering that require equation solving or optimization. Driven by its utility and mathematical curiosity, researchers over the years have developed a variety of generalized derivatives. In this thesis, we will first take a look at Clarke’s generalized derivative for locally Lipschitz continuous functions between Euclidean spaces, which roughly is the smallest convex set containing all nearby derivatives of a domain point of interest. Clarke’s generalized derivative in this setting possesses a strong theoretical and numerical toolkit, which is analogous to that of the classical derivative. It includes ...

An Introduction To Shape Dynamics, Patrick R. Kerrigan Nov 2019

#### An Introduction To Shape Dynamics, Patrick R. Kerrigan

##### Physics

Shape Dynamics (SD) is a new fundamental framework of physics which seeks to remove any non-relational notions from its methodology. importantly it does away with a background space-time and replaces it with a conceptual framework meant to reflect direct observables and recognize how measurements are taken. It is a theory of pure relationalism, and is based on different first principles then General Relativity (GR). This paper investigates how SD assertions affect dynamics of the three body problem, then outlines the shape reduction framework in a general setting.

Network Structure And Dynamics Of Biological Systems, Deena R. Schmidt Oct 2019

#### Network Structure And Dynamics Of Biological Systems, Deena R. Schmidt

##### Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.

Efficient Control Methods For Stochastic Boolean Networks, David Murrugarra Oct 2019

#### Efficient Control Methods For Stochastic Boolean Networks, David Murrugarra

##### Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.

Oct 2019

#### Topology And Dynamics Of Gene Regulatory Networks: A Meta-Analysis, Claus Kadelka

##### Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.

Oct 2019

#### Controllability And Observability Of Linear Nabla Discrete Fractional Systems, Tilekbek Zhoroev

##### Masters Theses & Specialist Projects

The main purpose of this thesis to examine the controllability and observability of the linear discrete fractional systems. First we introduce the problem and continue with the review of some basic definitions and concepts of fractional calculus which are widely used to develop the theory of this subject. In Chapter 3, we give the unique solution of the fractional difference equation involving the Riemann-Liouville operator of real order between zero and one. Additionally we study the sequential fractional difference equations and describe the way to obtain the state-space repre- sentation of the sequential fractional difference equations. In Chapter 4, we ...

#### From Optimization To Equilibration: Understanding An Emerging Paradigm In Artificial Intelligence And Machine Learning, Ian Gemp

##### Doctoral Dissertations

Many existing machine learning (ML) algorithms cannot be viewed as gradient descent on some single objective. The solution trajectories taken by these algorithms naturally exhibit rotation, sometimes forming cycles, a behavior that is not expected with (full-batch) gradient descent. However, these algorithms can be viewed more generally as solving for the equilibrium of a game with possibly multiple competing objectives. Moreover, some recent ML models, specifically generative adversarial networks (GANs) and its variants, are now explicitly formulated as equilibrium problems. Equilibrium problems present challenges beyond those encountered in optimization such as limit-cycles and chaotic attractors and are able to abstract ...

An Epidemiological Model With Simultaneous Recoveries, Ariel B. Farber Jun 2019

#### An Epidemiological Model With Simultaneous Recoveries, Ariel B. Farber

##### Electronic Theses and Dissertations

Epidemiological models are an essential tool in understanding how infection spreads throughout a population. Exploring the effects of varying parameters provides insight into the driving forces of an outbreak. In this thesis, an SIS (susceptible-infectious-susceptible) model is built partnering simulation methods, differential equations, and transition matrices with the intent to describe how simultaneous recoveries influence the spread of a disease in a well-mixed population. Individuals in the model transition between only two states; an individual is either susceptible — able to be infected, or infectious — able to infect others. Events in this model (infections and recoveries) occur by way of a ...

The Long-Run Effects Of Tropical Cyclones On Infant Mortality, Isabel Miranda May 2019

#### The Long-Run Effects Of Tropical Cyclones On Infant Mortality, Isabel Miranda

##### Master's Theses

In the United States alone, each tropical cyclone causes an average of \$14.6 billion worth of damages. In addition to the destruction of physical infrastructure, natural disasters also negatively impact human capital formation. These losses are often more difficult to observe, and therefore, are over looked when quantifying the true costs of natural disasters. One particular effect is an increase in infant mortality rates, an important indicator of a country’s general socioeconomic level. This paper utilizes a model created by Anttila-Hughes and Hsiang, that takes advantage of annual variation in tropical cyclones using annual spatial average maximum wind ...

#### Characterizing The Permanence And Stationary Distribution For A Family Of Malaria Stochastic Models, Divine Wanduku

##### Biology and Medicine Through Mathematics Conference

No abstract provided.

May 2019

#### Bifurcation Analysis Of A Photoreceptor Interaction Model For Retinitis Pigmentosa, Anca R. Radulescu

##### Biology and Medicine Through Mathematics Conference

No abstract provided.

Spiking Activity In Networks Of Neurons Impacted By Axonal Swelling, Brian Frost, Stan Mintchev May 2019

#### Spiking Activity In Networks Of Neurons Impacted By Axonal Swelling, Brian Frost, Stan Mintchev

##### Biology and Medicine Through Mathematics Conference

No abstract provided.

May 2019

#### Periodicity And Invertibility Of Lattice Gas Cellular Automata, Jiawen Wang

##### Mathematical Sciences Technical Reports (MSTR)

A cellular automaton is a type of mathematical system that models the behavior of a set of cells with discrete values in progressing time steps. The often complicated behaviors of cellular automata are studied in computer science, mathematics, biology, and other science related fields. Lattice gas cellular automata are used to simulate the movements of particles. This thesis aims to discuss the properties of lattice gas models, including periodicity and invertibility, and to examine their accuracy in reflecting the physics of particles in real life. Analysis of elementary cellular automata is presented to introduce the concept of cellular automata and ...

Apr 2019

#### Mathematical Models: The Lanchester Equations And The Zombie Apocalypse, Hailey Bauer

##### Undergraduate Theses and Capstone Projects

This research study used mathematical models to analyze and depicted specific battle situations and the outcomes of the zombie apocalypse. The original models that predicted warfare were the Lanchester models, while the zombie apocalypse models were fictional expansions upon mathematical models used to examine infectious diseases. In this paper, I analyzed and compared different mathematical models by examining each model’s set of assumptions and the impact of the change in variables on the population classes. The purpose of this study was to understand the basics of the discrete dynamical systems and to determine the similarities between imaginary and realistic ...

The Waiting Time And Dynamic Partitions, Akhtam Dzhalilov, Mukhriddin Khomidov Mar 2019

#### The Waiting Time And Dynamic Partitions, Akhtam Dzhalilov, Mukhriddin Khomidov

##### Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In the present paper we study the behaviour of normalized waiting times for linear irrational rotations. D.Kim and B.Seo investigated the waiting times for equidistance partitions. We consider waiting times with respect to dynamical partitions. The results show that limiting behaviour of waiting times essentially depend on type of partitions.

#### Analyzing A Method To Determine The Utility Of Adding A Classification System To A Sequence For Improved Accuracy, Kevin S. Pamilagas

##### Theses and Dissertations

Frequently, ensembles of classification systems are combined into a sequence in order to better enhance the accuracy in classifying objects of interest. However, there is a point in which adding an additional system to a sequence no longer enhances the system as either the increase in operational costs exceeds the benefit of improvements in classification or the addition of the system does not increase accuracy at all. This research will examine a utility measure to determine the valid or invalid nature of adding a classification system to a sequence of such systems based on the ratio of the change in ...

Wall Model Large Eddy Simulation Of A Diffusing Serpentine Inlet Duct, Ryan J. Thompson Mar 2019

#### Wall Model Large Eddy Simulation Of A Diffusing Serpentine Inlet Duct, Ryan J. Thompson

##### Theses and Dissertations

The modeling focus on serpentine inlet ducts (S-duct), as with any inlet, is to quantify the total pressure recovery and ow distortion after the inlet, which directly impacts the performance of a turbine engine fed by the inlet. Accurate prediction of S-duct ow has yet to be achieved amongst the computational fluid dynamics (CFD) community to improve the reliance on modeling reducing costly testing. While direct numerical simulation of the turbulent ow in an S-duct is too cost prohibitive due to grid scaling with Reynolds number, wall-modeled large eddy simulation (WM-LES) serves as a tractable alternative. US3D, a hypersonic research ...

New Experimental Investigations For The 3x+1 Problem: The Binary Projection Of The Collatz Map, Benjamin Bairrington, Aaron Okano Mar 2019

#### New Experimental Investigations For The 3x+1 Problem: The Binary Projection Of The Collatz Map, Benjamin Bairrington, Aaron Okano

The 3x + 1 Problem, or the Collatz Conjecture, was originally developed in the early 1930's. It has remained unsolved for over eighty years. Throughout its history, traditional methods of mathematical problem solving have only succeeded in proving heuristic properties of the mapping. Because the problem has proven to be so difficult to solve, many think it might be undecidable. In this paper we brie y follow the history of the 3x + 1 problem from its creation in the 1930's to the modern day. Its history is tied into the development of the Cosper Algorithm, which maps binary sequences ...

Large Scale Dynamical Model Of Macrophage/Hiv Interactions, Sean T. Bresnahan, Matthew M. Froid Mar 2019

#### Large Scale Dynamical Model Of Macrophage/Hiv Interactions, Sean T. Bresnahan, Matthew M. Froid

##### Student Research and Creative Activity Fair

Properties emerge from the dynamics of large-scale molecular networks that are not discernible at the individual gene or protein level. Mathematical models - such as probabilistic Boolean networks - of molecular systems offer a deeper insight into how these emergent properties arise. Here, we introduce a non-linear, deterministic Boolean model of protein, gene, and chemical interactions in human macrophage cells during HIV infection. Our model is composed of 713 nodes with 1583 interactions between nodes and is responsive to 38 different inputs including signaling molecules, bacteria, viruses, and HIV viral particles. Additionally, the model accurately simulates the dynamics of over 50 different ...

Local Lagged Adapted Generalized Method Of Moments And Applications, Olusegun Michael Otunuga, Gangaram S. Ladde, Nathan G. Ladde Feb 2019

#### Local Lagged Adapted Generalized Method Of Moments And Applications, Olusegun Michael Otunuga, Gangaram S. Ladde, Nathan G. Ladde

##### Olusegun Michael Otunuga

In this work, an attempt is made for developing the local lagged adapted generalized method of moments (LLGMM). This proposed method is composed of: (1) development of the stochastic model for continuous-time dynamic process, (2) development of the discrete-time interconnected dynamic model for statistic process, (3) utilization of Euler-type discretized scheme for nonlinear and non-stationary system of stochastic differential equations, (4) development of generalized method of moment/observation equations by employing lagged adaptive expectation process, (5) introduction of the conceptual and computational parameter estimation problem, (6) formulation of the conceptual and computational state estimation scheme and (7) definition of the ...

Stochastic Modeling Of Energy Commodity Spot Price Processes With Delay In Volatility, Olusegun Michael Otunuga, Gangaram S. Ladde Feb 2019

#### Stochastic Modeling Of Energy Commodity Spot Price Processes With Delay In Volatility, Olusegun Michael Otunuga, Gangaram S. Ladde

##### Olusegun Michael Otunuga

Employing basic economic principles, we systematically develop both deterministic and stochastic dynamic models for the log-spot price process of energy commodity. Furthermore, treating a diﬀusion coeﬃcient parameter in the non-seasonal log-spot price dynamic system as a stochastic volatility functional of log-spot price, an interconnected system of stochastic model for log-spot price, expected log-spot price and hereditary volatility process is developed. By outlining the risk-neutral dynamics and pricing, suﬃcient conditions are given to guarantee that the risk-neutral dynamic model is equivalent to the developed model. Furthermore, it is shown that the expectation of the square of volatility under the risk-neutral measure ...