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Dynamical Systems Commons

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336 full-text articles. Page 1 of 15.

Universality And Synchronization In Complex Quadratic Networks (Cqns), Anca R. Radulescu, Danae Evans 2022 State University of New York at New Paltz

Universality And Synchronization In Complex Quadratic Networks (Cqns), Anca R. Radulescu, Danae Evans

Biology and Medicine Through Mathematics Conference

No abstract provided.


Gene Drives And The Consequences Of Over-Suppression, Cole Butler 2022 Virginia Commonwealth University

Gene Drives And The Consequences Of Over-Suppression, Cole Butler

Biology and Medicine Through Mathematics Conference

No abstract provided.


Real-Time Interactive Simulation Of Large Bird Flocks: Toward Understanding Murmurations, Maxfield R. Comstock 2022 Georgia Institute of Technology

Real-Time Interactive Simulation Of Large Bird Flocks: Toward Understanding Murmurations, Maxfield R. Comstock

Biology and Medicine Through Mathematics Conference

No abstract provided.


The Butterfly Effect Of Fractals, Cody Watkins 2022 Murray State University

The Butterfly Effect Of Fractals, Cody Watkins

Honors College Theses

This thesis applies concepts in fractal geometry to the relatively new field of mathematics known as chaos theory, with emphasis on the underlying foundation of the field: the butterfly effect. We begin by reviewing concepts useful for an introduction to chaos theory by defining terms such as fractals, transformations, affine transformations, and contraction mappings, as well as proving and demonstrating the contraction mapping theorem. We also show that each fractal produced by the contraction mapping theorem is unique in its fractal dimension, another term we define. We then show and demonstrate iterated function systems and take a closer look at ...


Reduced-Order Dynamic Modeling And Robust Nonlinear Control Of Fluid Flow Velocity Fields, Anu Kossery Jayaprakash, William MacKunis, Vladimir Golubev, Oksana Stalnov 2021 Embry-Riddle Aeronautical University

Reduced-Order Dynamic Modeling And Robust Nonlinear Control Of Fluid Flow Velocity Fields, Anu Kossery Jayaprakash, William Mackunis, Vladimir Golubev, Oksana Stalnov

Publications

A robust nonlinear control method is developed for fluid flow velocity tracking, which formally addresses the inherent challenges in practical implementation of closed-loop active flow control systems. A key challenge being addressed here is flow control design to compensate for model parameter variations that can arise from actuator perturbations. The control design is based on a detailed reduced-order model of the actuated flow dynamics, which is rigorously derived to incorporate the inherent time-varying uncertainty in the both the model parameters and the actuator dynamics. To the best of the authors’ knowledge, this is the first robust nonlinear closed-loop active flow ...


A Connectivity Framework To Explore The Role Of Anthropogenic Activity And Climate On The Propagation Of Water And Sediment At The Catchment Scale, Christos Giannopoulos 2021 University of Tennessee, Knoxville

A Connectivity Framework To Explore The Role Of Anthropogenic Activity And Climate On The Propagation Of Water And Sediment At The Catchment Scale, Christos Giannopoulos

Doctoral Dissertations

Anthropogenic disturbance in intensively managed landscapes (IMLs) has dramatically altered critical zone processes, resulting in fundamental changes in material fluxes. Mitigating the negative effects of anthropogenic disturbance and making informed decisions for optimal placement and assessment of best management practices (BMPs) requires fundamental understanding of how different practices affect the connectivity or lack thereof of governing transport processes and resulting material fluxes across different landscape compartments within the hillslope-channel continuum of IMLs. However, there are no models operating at the event timescale that can accurately predict material flux transport from the hillslope to the catchment scale capturing the spatial and ...


An Integral Projection Model For Gizzard Shad That Includes Density-Dependent Age-0 Survival, James Peirce, Greg Sandland 2021 University of Wisconsin - La Crosse

An Integral Projection Model For Gizzard Shad That Includes Density-Dependent Age-0 Survival, James Peirce, Greg Sandland

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Biocontrol Of The Emerald Ash Borer: An Adapted Nicholson-Bailey Model, Michael Kerckhove, Shuheng Chen 2021 University of Richmond

Biocontrol Of The Emerald Ash Borer: An Adapted Nicholson-Bailey Model, Michael Kerckhove, Shuheng Chen

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Mathematical Model Describing The Behavior Of Biomass, Acidity, And Viscosity As A Function Of Temperature In The Shelf Life Of Yogurt, Manuel Alvarado, Paul A. Valle, Yolocuauhtli Salazar 2021 Durango Institute of Technology, México

Mathematical Model Describing The Behavior Of Biomass, Acidity, And Viscosity As A Function Of Temperature In The Shelf Life Of Yogurt, Manuel Alvarado, Paul A. Valle, Yolocuauhtli Salazar

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Mathematical Modeling Of Breast Cancer Cell Mcf-7 Growths Due To Curcumin Treatments, Widodo Samyono, Hildana Assefa, Kana Kassa 2021 Jarvis Christian College

Mathematical Modeling Of Breast Cancer Cell Mcf-7 Growths Due To Curcumin Treatments, Widodo Samyono, Hildana Assefa, Kana Kassa

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Hyperbolicity And Certain Statistical Properties Of Chaotic Billiard Systems, Kien T. Nguyen 2021 University of Massachusetts Amherst

Hyperbolicity And Certain Statistical Properties Of Chaotic Billiard Systems, Kien T. Nguyen

Doctoral Dissertations

In this thesis, we address some questions about certain chaotic dynamical systems. In particular, the objects of our studies are chaotic billiards. A billiard is a dynamical system that describe the motions of point particles in a table where the particles collide elastically with the boundary and with each other.

Among the dynamical systems, billiards have a very important position. They are models for many problems in acoustics, optics, classical and quantum mechanics, etc.. Despite of the rather simple description, billiards of different shapes of tables exhibit a wide range of dynamical properties from being complete integrable to chaotic. A ...


On The Rectilinear Motion Of Three Bodies Mutually Attracting Each Other, Sylvio R. Bistafa 2021 University of Sao Paulo

On The Rectilinear Motion Of Three Bodies Mutually Attracting Each Other, Sylvio R. Bistafa

Euleriana

This is an annotated translation from Latin of E327 -- De motu rectilineo trium corporum se mutuo attrahentium (“On the rectilinear motion of three bodies mutually attracting each other”). In this publication, Euler considers three bodies lying on a straight line, which are attracted to each other by central forces inversely proportional to the square of their separation distance (inverse-square law). Here Euler finds that the parameter that controls the relative distances among the bodies is given by a quintic function.


Mapping Polynomial Dynamics, Devin Becker 2021 DePaul University

Mapping Polynomial Dynamics, Devin Becker

DePaul Discoveries

We explore the complex dynamics of a family of polynomials defined on the complex plane by f(z) = azm(1+z/d)d where a is a complex number not equal to zero, and m and d are at least 2. These functions have three finite critical points, one of which has behavior that differs as we change our parameter values. We analyze the dynamical behavior at this critical point, with a particular interest in the structures that appear in the filled Julia set K(f) and the basin of infinity A_{\infty}(f). The behavior of the family ...


Contributions To The Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya 2021 Montclair State University

Contributions To The Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya

Department of Mathematics Facuty Scholarship and Creative Works

This issue showcases a compilation of papers on fluid mechanics (FM) education, covering different sub topics of the subject. The success of the first volume [1] prompted us to consider another follow-up special issue on the topic, which has also been very successful in garnering an impressive variety of submissions. As a classical branch of science, the beauty and complexity of fluid dynamics cannot be overemphasized. This is an extremely well-studied subject which has now become a significant component of several major scientific disciplines ranging from aerospace engineering, astrophysics, atmospheric science (including climate modeling), biological and biomedical science and engineering ...


Lebesgue Measure Preserving Thompson Monoid And Its Properties Of Decomposition And Generators, William Li 2021 Stanford University

Lebesgue Measure Preserving Thompson Monoid And Its Properties Of Decomposition And Generators, William Li

Rose-Hulman Undergraduate Mathematics Journal

This paper defines the Lebesgue measure preserving Thompson monoid, denoted by G, which is modeled on the Thompson group F except that the elements of G preserve the Lebesgue measure and can be non-invertible. The paper shows that any element of the monoid G is the composition of a finite number of basic elements of the monoid G and the generators of the Thompson group F. However, unlike the Thompson group F, the monoid G is not finitely generated. The paper then defines equivalence classes of the monoid G, use them to construct a monoid H that is finitely generated ...


Disjointness Of Linear Fractional Actions On Serre Trees, Henry W. Talbott 2021 Brown University

Disjointness Of Linear Fractional Actions On Serre Trees, Henry W. Talbott

Rose-Hulman Undergraduate Mathematics Journal

Serre showed that, for a discrete valuation field, the group of linear fractional transformations acts on an infinite regular tree with vertex degree determined by the residue degree of the field. Since the p-adics and the polynomials over the finite field of order p act on isomorphic trees, we may ask whether pairs of actions from these two groups are ever conjugate as tree automorphisms. We analyze permutations induced on finite vertex sets, and show a permutation classification result for actions by these linear fractional transformation groups. We prove that actions by specific subgroups of these groups are conjugate only ...


Smooth Global Approximation For Continuous Data Assimilation, Kenneth R. Brown 2021 CUNY Hunter College

Smooth Global Approximation For Continuous Data Assimilation, Kenneth R. Brown

Theses and Dissertations

This thesis develops the finite element method, constructs local approximation operators, and bounds their error. Global approximation operators are then constructed with a partition of unity. Finally, an application of these operators to data assimilation of the two-dimensional Navier-Stokes equations is presented, showing convergence of an algorithm in all Sobolev topologies.


Dynamic Parameter Estimation From Partial Observations Of The Lorenz System, Eunice Ng 2021 CUNY Hunter College

Dynamic Parameter Estimation From Partial Observations Of The Lorenz System, Eunice Ng

Theses and Dissertations

Recent numerical work of Carlson-Hudson-Larios leverages a nudging-based algorithm for data assimilation to asymptotically recover viscosity in the 2D Navier-Stokes equations as partial observations on the velocity are received continuously-in-time. This "on-the-fly" algorithm is studied both analytically and numerically for the Lorenz equations in this thesis.


On The Structure Of The Essential Spectrum For Discrete Schrödinger Operators Associated With Three-Particle System, Shukhrat Lakaev, Tirkash Radjabov, Nizomiddin Makhmasaitovich Aliev 2021 National University of Uzbekistan

On The Structure Of The Essential Spectrum For Discrete Schrödinger Operators Associated With Three-Particle System, Shukhrat Lakaev, Tirkash Radjabov, Nizomiddin Makhmasaitovich Aliev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

We consider a family of discrete Schrödinger operators $H(K),\,K\in (-\pi,\pi]^5$ associated with a system of three quantum particles on the five-dimensional lattice ${\mathbb{Z}}^5$ interacting via short-range pair potentials and having arbitrary "dispersion functions" with not necessarily compact support.

We show that the essential spectrum of the three-particle discrete Schr\"odinger operator $H(K),\,K\in (-\pi,\pi]^5$ consists of a finitely many bounded closed intervals.


Stationary Probability Distributions Of Stochastic Gradient Descent And The Success And Failure Of The Diffusion Approximation, William Joseph McCann 2021 New Jersey Institute of Technology

Stationary Probability Distributions Of Stochastic Gradient Descent And The Success And Failure Of The Diffusion Approximation, William Joseph Mccann

Theses

In this thesis, Stochastic Gradient Descent (SGD), an optimization method originally popular due to its computational efficiency, is analyzed using Markov chain methods. We compute both numerically, and in some cases analytically, the stationary probability distributions (invariant measures) for the SGD Markov operator over all step sizes or learning rates. The stationary probability distributions provide insight into how the long-time behavior of SGD samples the objective function minimum.

A key focus of this thesis is to provide a systematic study in one dimension comparing the exact SGD stationary distributions to the Fokker-Planck diffusion approximation equations —which are commonly used in ...


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