Dynamical Systems Commons^™

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.

Fluids In Music: The Mathematics Of Pan’S Flutes, Bogdan Nita, Sajan Ramanathan

Department of Mathematics Faculty Scholarship and Creative Works

We discuss the mathematics behind the Pan’s flute. We analyze how the sound is created, the relationship between the notes that the pipes produce, their frequencies and the length of the pipes. We find an equation which models the curve that appears at the bottom of any Pan’s flute due to the different pipe lengths.

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

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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 …

Dynamics Of The Family Lambda Tan Z^2, Santanu Nandi

Dissertations, Theses, and Capstone Projects

We prove some topological properties of the dynamical plane ($z$-plane) and a combinatorial structure of the parameter plane of a holomorphic family of meromorphic maps $\lambda \tan z^2$. In the dynamical plane, we prove that there is no Herman ring and the Julia set is a Cantor set for the map when the parameter is in the central capture component. Julia set is connected for the maps when the parameters are in other hyperbolic components. In the parameter plane, I prove that the capture components are simply connected and there are always four hyperbolic shell components attached to a virtual …

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 speeds and …

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

Biology and Medicine Through Mathematics Conference

No abstract provided.

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

Biology and Medicine Through Mathematics Conference

No abstract provided.

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 …

Dynamic Attribute-Level Best Worst Discrete Choice Experiments, Amanda Working, Mohammed Alqawba, Norou Diawara

Mathematics & Statistics Faculty Publications

Dynamic modelling of decision maker choice behavior of best and worst in discrete choice experiments (DCEs) has numerous applications. Such models are proposed under utility function of decision maker and are used in many areas including social sciences, health economics, transportation research, and health systems research. After reviewing references on the study of such experiments, we present example in DCE with emphasis on time dependent best-worst choice and discrimination between choice attributes. Numerical examples of the dynamic DCEs are simulated, and the associated expected utilities over time of the choice models are derived using Markov decision processes. The estimates are …

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 models. …

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

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

Rose-Hulman Undergraduate Mathematics Journal

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

UNO 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 …

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 highlights …

Role Of Combinatorial Complexity In Genetic Networks, Sharon Yang

SMU Journal of Undergraduate Research

A common motif found in genetic networks is the formation of large complexes. One difficulty in modeling this motif is the large number of possible intermediate complexes that can form. For instance, if a complex could contain up to 10 different proteins, 210 possible intermediate complexes can form. Keeping track of all complexes is difficult and often ignored in mathematical models. Here we present an algorithm to code ordinary differential equations (ODEs) to model genetic networks with combinatorial complexity. In these routines, the general binding rules, which counts for the majority of the reactions, are implemented automatically, thus the users …

Local Lagged Adapted Generalized Method Of Moments: An Innovative Estimation And Forecasting Approach And Its Applications., Olusegun Michael Otunuga, Gandaram S. Ladde, Nathan G. Ladde

Mathematics Faculty Research

In this work, an attempt is made to apply the Local Lagged Adapted Generalized Method of Moments (LLGMM) to estimate state and parameters in stochastic differential dynamic models. The development of LLGMM is motivated by parameter and state estimation problems in continuous-time nonlinear and non-stationary stochastic dynamic model validation problems in biological, chemical, engineering, energy commodity markets, financial, medical, military, physical sciences and social sciences. The byproducts of this innovative approach (LLGMM) are the balance between model specification and model prescription of continuous-time dynamic process and the development of discrete-time interconnected dynamic model of local sample mean and variance statistic …

Hidden Symmetries In Classical Mechanics And Related Number Theory Dynamical System, Mohsin Md Abdul Karim

Masters Theses

Classical Mechanics consists of three parts: Newtonian, Lagrangian and Hamiltonian Mechanics, where each part is a special extension of the previous part. Each part has explicit symmetries (the explicit Laws of Motion), which, in turn, generate implicit or hidden symmetries (like the Law of Conservation of Energy, etc). In this Master's Thesis, different types of hidden symmetries are considered; they are reflected in the Noether Theorem and the Poincare Recurrence Theorem applied to Lagrangian and Hamiltonian Systems respectively.

The Poincare Recurrence Theorem is also applicable to some number theory problems, which can be considered as dynamical systems. In …