The Long-Run Effects Of Tropical Cyclones On Infant Mortality, 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 ...

Characterizing The Permanence And Stationary Distribution For A Family Of Malaria Stochastic Models, 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.

School Policy Evaluated With Time-Reversible Markov Chain, 2019 University of Connecticut - Storrs

#### School Policy Evaluated With Time-Reversible Markov Chain, Trajan Murphy, Iddo Ben-Ari

*Honors Scholar Theses*

In this work we propose a reversible Markov chain scheme to model for the mobility of students affected by a grade school leveling policy. This model provides unified and mathematically tractable framework in which transition functions are sampled uniformly from the set of {\bf reversible} transition functions. The results from the study appear to confirm the disadvantageous effects of this school policy, on par with the of a previous model on the same policy.

Topology And Dynamics Of Gene Regulatory Networks: A Meta-Analysis, 2019 Iowa State University

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

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Predicting Dynamics From Hardwiring In Canonical Low-Dimensional Coupled Networks, 2019 State University of New York at New Paltz

#### Predicting Dynamics From Hardwiring In Canonical Low-Dimensional Coupled Networks, Anca R. Radulescu

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Quantifying Complex Systems Via Computational Fly Swarms, 2019 Linfield College

#### Quantifying Complex Systems Via Computational Fly Swarms, Troy Taylor

*Senior Theses*

Complexity is prevalent both in natural and in human-made systems, yet is not well understood quantitatively. Qualitatively, complexity describes a phenomena in which a system composed of individual pieces, each having simple interactions with one another, results in interesting bulk properties that would otherwise not exist. One example of a complex biological system is the bird flock, in particular, a starling murmuration. Starlings are known to move in the direction of their neighbors and avoid collisions with fellow starlings, but as a result of these simple movement choices, the flock as a whole tends to exhibit fluid-like movements and form ...

The Effects Of Finite Precision On The Simulation Of The Double Pendulum, 2019 James Madison University

#### The Effects Of Finite Precision On The Simulation Of The Double Pendulum, Rebecca Wild

*Senior Honors Projects, 2010-current*

We use mathematics to study physical problems because abstracting the information allows us to better analyze what could happen given any range and combination of parameters. The problem is that for complicated systems mathematical analysis becomes extremely cumbersome. The only effective and reasonable way to study the behavior of such systems is to simulate the event on a computer. However, the fact that the set of floating-point numbers is finite and the fact that they are unevenly distributed over the real number line raises a number of concerns when trying to simulate systems with chaotic behavior. In this research we ...

Mathematical Models: The Lanchester Equations And The Zombie Apocalypse, 2019 University of Lynchburg

#### 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 ...

Parameter Estimation And Optimal Design Techniques To Analyze A Mathematical Model In Wound Healing, 2019 Western Kentucky University

#### Parameter Estimation And Optimal Design Techniques To Analyze A Mathematical Model In Wound Healing, Nigar Karimli

*Masters Theses & Specialist Projects*

For this project, we use a modified version of a previously developed mathematical model, which describes the relationships among matrix metalloproteinases (MMPs), their tissue inhibitors (TIMPs), and extracellular matrix (ECM). Our ultimate goal is to quantify and understand differences in parameter estimates between patients in order to predict future responses and individualize treatment for each patient. By analyzing parameter confidence intervals and confidence and prediction intervals for the state variables, we develop a parameter space reduction algorithm that results in better future response predictions for each individual patient. Moreover, use of another subset selection method, namely Structured Covariance Analysis, that ...

Modelling Non-Linear Functional Responses In Competitive Biological Systems., 2019 Western University

#### Modelling Non-Linear Functional Responses In Competitive Biological Systems., Nickolas Goncharenko

*Western Research Forum*

One of the most versatile and well understood models in mathematical biology is the Competitive Lotka Volterra (CLV) model, which describes the behaviour of any number of exclusively competitive species (that is each species competes directly with every other species). Despite it's success in describing many phenomenon in biology, chemistry and physics the CLV model cannot describe any non-linear environmental effects (including resource limitation and immune response of a host due to infection). The reason for this is the theory monotone dynamical systems, which was codeveloped with the CLV model, does not apply when this non-linear effect is introduced ...

Climate Change In A Differential Equations Course: Using Bifurcation Diagrams To Explore Small Changes With Big Effects, 2019 Frostburg State University

#### Climate Change In A Differential Equations Course: Using Bifurcation Diagrams To Explore Small Changes With Big Effects, Justin Dunmyre, Nicholas Fortune, Tianna Bogart, Chris Rasmussen, Karen Keene

*CODEE Journal*

The environmental phenomenon of climate change is of critical importance to today's science and global communities. Differential equations give a powerful lens onto this phenomenon, and so we should commit to discussing the mathematics of this environmental issue in differential equations courses. Doing so highlights the power of linking differential equations to environmental and social justice causes, and also brings important science to the forefront in the mathematics classroom. In this paper, we provide an extended problem, appropriate for a first course in differential equations, that uses bifurcation analysis to study climate change. Specifically, through studying hysteresis, this problem ...

Practical Chaos: Using Dynamical Systems To Encrypt Audio And Visual Data, 2019 Scripps College

#### 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.

Riemann-Hilbert Problem, Integrability And Reductions, 2019 Institute of Mathematics and Informatics, Bulgarian Academy of Sciences

#### Riemann-Hilbert Problem, Integrability And Reductions, Vladimir Gerdjikov, Rossen Ivanov, Aleksander Stefanov

*Articles*

Abstract. The present paper is dedicated to integrable models with Mikhailov reduction groups *G _{R} ≃ D_{h}*. Their Lax representation allows us to prove, that their solution is equivalent to solving Riemann-Hilbert problems, whose contours depend on the realization of the G

_{R}-action on the spectral parameter. Two new examples of Nonlinear Evolution Equations (NLEE) with

*D*symmetries are presented.

_{h}Surface Waves Over Currents And Uneven Bottom, 2019 University College Cork

#### Surface Waves Over Currents And Uneven Bottom, Alan C. Compelli, Rossen Ivanov, Calin I. Martin, Michail D. Todorov

*Articles*

The propagation of surface water waves interacting with a current and an uneven bottom is studied. Such a situation is typical for ocean waves where the winds generate currents in the top layer of the ocean. The role of the bottom topography is taken into account since it also influences the local wave and current patterns. Specific scaling of the variables is selected which leads to approximations of Boussinesq and KdV types. The arising KdV equation with variable coefficients, dependent on the bottom topography, is studied numerically when the initial condition is in the form of the one soliton solution ...

Multiscale Mathematical Modelling Of Nonlinear Nanowire Resonators For Biological Applications, 2019 Wilfrid Laurier University

#### Multiscale Mathematical Modelling Of Nonlinear Nanowire Resonators For Biological Applications, Rosa Fallahpourghadikolaei

*Theses and Dissertations (Comprehensive)*

Nanoscale systems fabricated with low-dimensional nanostructures such as carbon nanotubes, nanowires, quantum dots, and more recently graphene sheets, have fascinated researchers from different fields due to their extraordinary and unique physical properties. For example, the remarkable mechanical properties of nanoresonators empower them to have a very high resonant frequency up to the order of giga to terahertz. The ultra-high frequency of these systems attracted the attention of researchers in the area of bio-sensing with the idea to implement them for detection of tiny bio-objects. In this thesis, we originally propose and analyze a mathematical model for nonlinear vibrations of nanowire ...

Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, 2018 Wojciech Budzianowski Consulting Services

#### Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

A Companion To The Introduction To Modern Dynamics, 2018 Purdue University

#### A Companion To The Introduction To Modern Dynamics, David D. Nolte

*David D Nolte*

*Introduction to Modern Dynamics: Chaos, Networks, Space and Time*(Oxford University Press, 2019).

17 - Stability Analysis Of Stochastically Switching Kuramoto Networks, 2018 Georgia State University

#### 17 - Stability Analysis Of Stochastically Switching Kuramoto Networks, Ratislav Krylov, Igor Belykh Prof.

*Georgia Undergraduate Research Conference (GURC)*

Motivated by real-world networks with evolving connections, we analyze how stochastic switching affects patterns of synchrony and their stability in networks of identical Kuramoto oscillators with inertia. Stochastic dynamical networks are a useful model for many physical, biological, and engineering systems that have evolving topology, but they have proven to be difficult to work with, and the analytical results are rare. These networks have two characteristic time scales, one is associated with intrinsic dynamics of individual oscillators comprising the network, and the other corresponds to switching period of on-off connections. In the limit of fast switching, the relation between the ...

Bifurcation Analysis Of Two Biological Systems: A Tritrophic Food Chain Model And An Oscillating Networks Model, 2018 The University of Western Ontario

#### Bifurcation Analysis Of Two Biological Systems: A Tritrophic Food Chain Model And An Oscillating Networks Model, Xiangyu Wang

*Electronic Thesis and Dissertation Repository*

In this thesis, we apply bifurcation theory to study two biological systems. Main attention is focused on complex dynamical behaviors such as stability and bifurcation of limit cycles. Hopf bifurcation is particularly considered to show bistable or even tristable phenomenon which may occur in biological systems. Recurrence is also investigated to show that such complex behavior is common in biological systems.

First we consider a tritrophic food chain model with Holling functional response types III and IV for the predator and superpredator, respectively. Main attention is focused on the sta- bility and bifurcation of equilibria when the prey has a ...

The Influence Of Canalization On The Robustness Of Finite Dynamical Systems, 2018 Illinois State University

#### The Influence Of Canalization On The Robustness Of Finite Dynamical Systems, Claus Kadelka

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

No abstract provided.