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Non-linear Dynamics Commons

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The Computational Study Of Fly Swarms & Complexity, Austin Bebee 2018 Linfield College

The Computational Study Of Fly Swarms & Complexity, Austin Bebee

Senior Theses

A system is considered complex if it is composed of individual parts that abide by their own set of rules, while the system, as a whole, will produce non-deterministic properties. This prevents the behavior of such systems from being accurately predicted. The motivation for studying complexity spurs from the fact that it is a fundamental aspect of innumerable systems. Among complex systems, fly swarms are relatively simple, but even so they are still not well understood. In this research, several computational models were developed to assist with the understanding of fly swarms. These models were primarily analyzed by using the ...


Physical Applications Of The Geometric Minimum Action Method, George L. Poppe Jr. 2018 The Graduate Center, City University of New York

Physical Applications Of The Geometric Minimum Action Method, George L. Poppe Jr.

All Dissertations, Theses, and Capstone Projects

This thesis extends the landscape of rare events problems solved on stochastic systems by means of the \textit{geometric minimum action method} (gMAM). These include partial differential equations (PDEs) such as the real Ginzburg-Landau equation (RGLE), the linear Schroedinger equation, along with various forms of the nonlinear Schroedinger equation (NLSE) including an application towards an ultra-short pulse mode-locked laser system (MLL).

Additionally we develop analytical tools that can be used alongside numerics to validate those solutions. This includes the use of instanton methods in deriving state transitions for the linear Schroedinger equation and the cubic diffusive NLSE.

These analytical solutions ...


Iterative Methods To Solve Systems Of Nonlinear Algebraic Equations, Md Shafiful Alam 2018 Western Kentucky University

Iterative Methods To Solve Systems Of Nonlinear Algebraic Equations, Md Shafiful Alam

Masters Theses & Specialist Projects

Iterative methods have been a very important area of study in numerical analysis since the inception of computational science. Their use ranges from solving algebraic equations to systems of differential equations and many more. In this thesis, we discuss several iterative methods, however our main focus is Newton's method. We present a detailed study of Newton's method, its order of convergence and the asymptotic error constant when solving problems of various types as well as analyze several pitfalls, which can affect convergence. We also pose some necessary and sufficient conditions on the function f for higher order of ...


P-46 A Periodic Matrix Model Of Seabird Behavior And Population Dynamics, Mykhaylo M. Malakhov, Benjamin MacDonald, Shandelle M. Henson, J. M. Cushing 2018 Andrews University

P-46 A Periodic Matrix Model Of Seabird Behavior And Population Dynamics, Mykhaylo M. Malakhov, Benjamin Macdonald, Shandelle M. Henson, J. M. Cushing

Honors Scholars & Undergraduate Research Poster Symposium Programs

Rising sea surface temperatures (SSTs) in the Pacific Northwest lead to food resource reductions for surface-feeding seabirds, and have been correlated with several marked behavioral changes. Namely, higher SSTs are associated with increased egg cannibalism and egg-laying synchrony in the colony. We study the long-term effects of climate change on population dynamics and survival by considering a simplified, cross-season model that incorporates both of these behaviors in addition to density-dependent and environmental effects. We show that cannibalism can lead to backward bifurcations and strong Allee effects, allowing the population to survive at lower resource levels than would be possible otherwise.


Theoretical Analysis Of Nonlinear Differential Equations, Emily Jean Weymier 2018 Stephen F Austin State University

Theoretical Analysis Of Nonlinear Differential Equations, Emily Jean Weymier

Electronic Theses and Dissertations

Nonlinear differential equations arise as mathematical models of various phenomena. Here, various methods of solving and approximating linear and nonlinear differential equations are examined. Since analytical solutions to nonlinear differential equations are rare and difficult to determine, approximation methods have been developed. Initial and boundary value problems will be discussed. Several linear and nonlinear techniques to approximate or solve the linear or nonlinear problems are demonstrated. Regular and singular perturbation theory and Magnus expansions are our particular focus. Each section offers several examples to show how each technique is implemented along with the use of visuals to demonstrate the accuracy ...


Particle Filters For State Estimation Of Confined Aquifers, Graeme Field 2018 University of North Florida

Particle Filters For State Estimation Of Confined Aquifers, Graeme Field

UNF Graduate Theses and Dissertations

Mathematical models are used in engineering and the sciences to estimate properties of systems of interest, increasing our understanding of the surrounding world and driving technological innovation. Unfortunately, as the systems of interest grow in complexity, so to do the models necessary to accurately describe them. Analytic solutions for problems with such models are provably intractable, motivating the use of approximate yet still accurate estimation techniques. Particle filtering methods have emerged as a popular tool in the presence of such models, spreading from its origins in signal processing to a diverse set of fields throughout engineering and the sciences including ...


Hopf Bifurcation Analysis Of Chaotic Chemical Reactor Model, Daniel Mandragona 2018 University of Central Florida

Hopf Bifurcation Analysis Of Chaotic Chemical Reactor Model, Daniel Mandragona

Honors in the Major Theses

Bifurcations in Huang's chaotic chemical reactor system leading from simple dynamics into chaotic regimes are considered. Following the linear stability analysis, the periodic orbit resulting from a Hopf bifurcation of any of the six fixed points is constructed analytically by the method of multiple scales across successively slower time scales, and its stability is then determined by the resulting final secularity condition. Furthermore, we run numerical simulations of our chemical reactor at a particular fixed point of interest, alongside a set of parameter values that forces our system to undergo Hopf bifurcation. These numerical simulations then verify our analysis ...


Reduced Models Of Point Vortex Systems In Quasigeostrophic Fluid Dynamics, Jonathan Maack 2018 University of Massachusetts Amherst

Reduced Models Of Point Vortex Systems In Quasigeostrophic Fluid Dynamics, Jonathan Maack

Doctoral Dissertations

We develop a nonequilibrium statistical mechanical description of the evolution of point vortex systems governed by either the Euler, single-layer quasigeostrophic or two-layer quasigeostrophic equations. Our approach is based on a recently proposed optimal closure procedure for deriving reduced models of Hamiltonian systems. In this theory the statistical evolution is kept within a parametric family of distributions based on the resolved variables chosen to describe the macrostate of the system. The approximate evolution is matched as closely as possible to the true evolution by minimizing the mean-squared residual in the Liouville equation, a metric which quantifies the information loss rate ...


Call For Abstracts - Resrb 2018, June 18-20, Brussels, Belgium, Wojciech M. Budzianowski 2017 Wojciech Budzianowski Consulting Services

Call For Abstracts - Resrb 2018, June 18-20, Brussels, Belgium, Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.


Rogue Rotary - Modular Robotic Rotary Joint Design, Sean Wesley Murphy, Tyler David Riessen, Jacob Mark Triplett 2017 California Polytechnic State University, San Luis Obispo

Rogue Rotary - Modular Robotic Rotary Joint Design, Sean Wesley Murphy, Tyler David Riessen, Jacob Mark Triplett

Mechanical Engineering

This paper describes the design process from ideation to test validation for a singular robotic joint to be configured into a myriad of system level of robots.


On The Existence Of Bogdanov-Takens Bifurcations, Zachary Deskin 2017 Missouri State University

On The Existence Of Bogdanov-Takens Bifurcations, Zachary Deskin

MSU Graduate Theses

In bifurcation theory, there is a theorem (called Sotomayor's Theorem) which proves the existence of one of three possible bifurcations of a given system, provided that certain conditions of the system are satisfied. It turns out that there is a "similar" theorem for proving the existence of what is referred to as a Bogdanov-Takens bifurcation. The author is only aware of one reference that has the proof of this theorem. However, most of the details were left out of the proof. The contribution of this thesis is to provide the details of the proof on the existence of Bogdanov-Takens ...


Examining The Electrical Excitation, Calcium Signaling, And Mechanical Contraction Cycle In A Heart Cell, Kristen Deetz, Nygel Foster, Darius Leftwich, Chad Meyer, Shalin Patel, Carlos Barajas, Matthias K. Gobbert, Zana Coulibaly 2017 Eastern University

Examining The Electrical Excitation, Calcium Signaling, And Mechanical Contraction Cycle In A Heart Cell, Kristen Deetz, Nygel Foster, Darius Leftwich, Chad Meyer, Shalin Patel, Carlos Barajas, Matthias K. Gobbert, Zana Coulibaly

Spora: A Journal of Biomathematics

As the leading cause of death in the United States, heart disease has become a principal concern in modern society. Cardiac arrhythmias can be caused by a dysregulation of calcium dynamics in cardiomyocytes. Calcium dysregulation, however, is not yet fully understood and is not easily predicted; this provides motivation for the subsequent research. Excitation-contraction coupling (ECC) is the process through which cardiomyocytes undergo contraction from an action potential. Calcium induced calcium release (CICR) is the mechanism through which electrical excitation is coupled with mechanical contraction through calcium signaling. The study of the interplay between electrical excitation, calcium signaling, and mechanical ...


Distributed Evolution Of Spiking Neuron Models On Apache Mahout For Time Series Analysis, Andrew Palumbo 2017 Cylance, Inc.

Distributed Evolution Of Spiking Neuron Models On Apache Mahout For Time Series Analysis, Andrew Palumbo

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Agent-Based Model For Integrated Pest Management With Periodic Control Strategies, Timothy Comar, Elizabeth Rodriguez 2017 Benedictine University

Agent-Based Model For Integrated Pest Management With Periodic Control Strategies, Timothy Comar, Elizabeth Rodriguez

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Stochastic And Deterministic Multigroup Epidemiology, Jordan Hasler, Chris Chang, Ananya Yammanuru, Lewis Oh, Esther Matthew, Mounisha Kovour 2017 Illinois Mathematics and Science Academy

Stochastic And Deterministic Multigroup Epidemiology, Jordan Hasler, Chris Chang, Ananya Yammanuru, Lewis Oh, Esther Matthew, Mounisha Kovour

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


A Critical Firing Rate In Synchronous Transitions Of Coupled Neurons, Annabelle Shaffer, Epaminondas Rosa, Rosangela Follmann 2017 Illinois State University

A Critical Firing Rate In Synchronous Transitions Of Coupled Neurons, Annabelle Shaffer, Epaminondas Rosa, Rosangela Follmann

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Handicap Principle Implies Emergence Of Dimorphic Ornaments, Sara Clifton, Daniel M. Abrams, Rosemary I. Braun 2017 Northwestern University

Handicap Principle Implies Emergence Of Dimorphic Ornaments, Sara Clifton, Daniel M. Abrams, Rosemary I. Braun

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Food Web Control And Synchronization Using A Robust Feedback, Hector Puebla, Mariana Rodriguez-Jara, Cesar S. Lopez-Monsalvo, Eliseo Hernandez-Martinez, Alejandra Velasco-Perez 2017 Universidad Autonoma Metropolitana

Food Web Control And Synchronization Using A Robust Feedback, Hector Puebla, Mariana Rodriguez-Jara, Cesar S. Lopez-Monsalvo, Eliseo Hernandez-Martinez, Alejandra Velasco-Perez

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


The Effects Of Evolution On Food Web Diversity And Abundance, Rosalyn Rael 2017 Tulane University of Louisiana

The Effects Of Evolution On Food Web Diversity And Abundance, Rosalyn Rael

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Modeling The Influence Of El Niño On Parasite Transmission In Sand Crab Populations And Seabird Abundance Along The California Coast, James Peirce, Olcay Akman, Abou Seck 2017 University of Wisconsin-La Crosse

Modeling The Influence Of El Niño On Parasite Transmission In Sand Crab Populations And Seabird Abundance Along The California Coast, James Peirce, Olcay Akman, Abou Seck

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


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