# Dynamical Systems Commons™

## All Articles in Dynamical Systems

296 full-text articles. Page 1 of 13.

2020 The Graduate Center, City University of New York

#### 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, 2020 University of Pittsburgh

#### 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, 2020 St. Olaf College

#### 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, 2020 University of California Berkeley

#### 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, 2020 University of Nebraska - Lincoln

#### 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, 2020 Rose-Hulman Institute of Technology

#### 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, 2020 Marshall University

#### 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 ...

2020 Bowdoin College

#### 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, 2020 Electric Power Group, LLC

#### 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 ...

2019 University of Maine

#### 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, 2019 California Polytechnic State University, San Luis Obispo

#### 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, 2019 University of Nevada, Reno

#### 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, 2019 University of Kentucky

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

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

No abstract provided.

2019 Illinois State University

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

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

No abstract provided.

2019 Western Kentucky University

#### 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 ...

2019 University of Massachusetts Amherst

#### 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, 2019 University of Maine

#### 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 ...

2019 The University of San Francisco

#### 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 ...

2019 Virginia Commonwealth University

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

##### Biology and Medicine Through Mathematics Conference

No abstract provided.

2019 State University of New York at New Paltz

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

##### Biology and Medicine Through Mathematics Conference

No abstract provided.