# Dynamical Systems Commons™

## All Articles in Dynamical Systems

244 full-text articles. Page 2 of 11.

Models Of Nation-Building Via Systems Of Differential Equations, 2017 Cedarville University

#### Models Of Nation-Building Via Systems Of Differential Equations, Carissa F. Slone, Darryl K. Ahner, Mark E. Oxley, William P. Baker

##### The Research and Scholarship Symposium

Nation-building modeling is an important field of research given the increasing number of candidate nations and the limited resources available. A modeling methodology and a system of differential equations model are presented to investigate the dynamics of nation-building. The methodology is based upon parameter identification techniques applied to a system of differential equations, to evaluate nation-building operations. Data from Operation Iraqi Freedom (OIF) and Afghanistan are used to demonstrate the validity of different models as well as the comparison of models.

Generalized Thomas-Fermi Equations As The Lampariello Class Of Emden-Fowler Equations, 2017 IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica

#### Generalized Thomas-Fermi Equations As The Lampariello Class Of Emden-Fowler Equations, Haret C. Rosu, Stefan C. Mancas

##### Publications

A one-parameter family of Emden-Fowler equations defined by Lampariello’s parameter p which, upon using Thomas-Fermi boundary conditions, turns into a set of generalized Thomas-Fermi equations comprising the standard Thomas-Fermi equation for p = 1 is studied in this paper. The entire family is shown to be non integrable by reduction to the corresponding Abel equations whose invariants do not satisfy a known integrability condition. We also discuss the equivalent dynamical system of equations for the standard Thomas-Fermi equation and perform its phase-plane analysis. The results of the latter analysis are similar for the whole class.

The Battle Against Malaria: A Teachable Moment, 2017 Schoolcraft College

#### The Battle Against Malaria: A Teachable Moment, Randy K. Schwartz

##### Journal of Humanistic Mathematics

Malaria has been humanity’s worst public health problem throughout recorded history. Mathematical methods are needed to understand which factors are relevant to the disease and to develop counter-measures against it. This article and the accompanying exercises provide examples of those methods for use in lower- or upper-level courses dealing with probability, statistics, or population modeling. These can be used to illustrate such concepts as correlation, causation, conditional probability, and independence. The article explains how the apparent link between sickle cell trait and resistance to malaria was first verified in Uganda using the chi-squared probability distribution. It goes on to ...

Data Predictive Control For Building Energy Management, 2017 University of Pennsylvania

#### Data Predictive Control For Building Energy Management, Achin Jain, Madhur Behl, Rahul Mangharam

##### Real-Time and Embedded Systems Lab (mLAB)

Decisions on how to best optimize energy systems operations are becoming ever so complex and conflicting, that model-based predictive control (MPC) algorithms must play an important role. However, a key factor prohibiting the widespread adoption of MPC in buildings, is the cost, time, and effort associated with learning first-principles based dynamical models of the underlying physical system. This paper introduces an alternative approach for implementing finite-time receding horizon control using control-oriented data-driven models. We call this approach Data Predictive Control (DPC). Specifically, by utilizing separation of variables, two novel algorithms for implementing DPC using a single regression tree and with ...

C.V. - Wojciech Budzianowski, 2017 Wojciech Budzianowski Consulting Services

#### C.V. - Wojciech Budzianowski, Wojciech M. Budzianowski

##### Wojciech Budzianowski

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Renewable Energy And Sustainable Development (Resd) Group, 2017 Wroclaw University of Technology

#### Renewable Energy And Sustainable Development (Resd) Group, Wojciech M. Budzianowski

##### Wojciech Budzianowski

No abstract provided.

2017 University of Kentucky

#### Orbital Stability Results For Soliton Solutions To Nonlinear Schrödinger Equations With External Potentials, Joseph B. Lindgren

##### Theses and Dissertations--Mathematics

For certain nonlinear Schroedinger equations there exist solutions which are called solitary waves. Addition of a potential $V$ changes the dynamics, but for small enough $||V||_{L^\infty}$ we can still obtain stability (and approximately Newtonian motion of the solitary wave's center of mass) for soliton-like solutions up to a finite time that depends on the size and scale of the potential $V$. Our method is an adaptation of the well-known Lyapunov method.

For the sake of completeness, we also prove long-time stability of traveling solitons in the case $V=0$.

Local Sensitivity Analysis Of Acute Inflammation, 2017 Marshall University

#### Local Sensitivity Analysis Of Acute Inflammation, James Martin

##### Theses, Dissertations and Capstones

The inflammatory response is the body's response to some pathogen or foreign invader. When infected by a pathogen, a healthy individual will mount a response with immunological factors to eliminate it. An inflammatory response that is either too strong or too weak can be detrimental to the individual's health. We will look at a qualitative mathematical model of the inflammatory response, in scenarios that represent varying disorders of the immune system. Using sensitivity analysis we determine which parameters of this model are most influential in the different scenarios. By determining which parameters are most influential we can suggest ...

Proceedings Of The 2nd Resrb 2017 Conference, June 19-21, 2017, Wrocław, Poland, 2016 Wojciech Budzianowski Consulting Services

#### Proceedings Of The 2nd Resrb 2017 Conference, June 19-21, 2017, Wrocław, Poland, Wojciech M. Budzianowski

##### Wojciech Budzianowski

No abstract provided.

Fractal Analysis Of Dna Sequences, 2016 Universidad del Valle - Colombia - Georgia Institute of Technology

#### Fractal Analysis Of Dna Sequences, Christian G. Arias, Pedro Antonio Moreno Phd, Carlos Tellez

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

No abstract provided.

Predator-Prey Dynamics With Intraspecific Competition And An Allee Effect In The Predator Population, 2016 The New School

#### Predator-Prey Dynamics With Intraspecific Competition And An Allee Effect In The Predator Population, Anne E. Yust, Erin N. Bodine

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

No abstract provided.

2016 University of Dayton

#### On The Perfect Reconstruction Of The Structure Of Dynamic Networks, Alan Veliz-Cuba

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

No abstract provided.

2016 Unity College

#### Comparing The Effects Of General And Selective Culling On Chronic Wasting Disease (Cwd) Prevalence, Elliott J. Moran

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

No abstract provided.

2016 Southeast University

#### Dem-Cfd Numerical Simulation And Experimental Validation Of Heat Transfer And Two-Component Flow In Fluidized Bed, Feihong Guo

##### The 8th International Conference on Physical and Numerical Simulation of Materials Processing

No abstract provided.

2016 The Graduate Center, City University of New York

#### The Fourth Movement Of György Ligeti's Piano Concerto: Investigating The Musical-Mathematical Connection, Cynthia L. Wong

##### All Dissertations, Theses, and Capstone Projects

This interdisciplinary study explores musical-mathematical analogies in the fourth movement of Ligeti’s Piano Concerto. Its aim is to connect musical analysis with the piece’s mathematical inspiration. For this purpose, the dissertation is divided into two sections. Part I (Chapters 1-2) provides musical and mathematical context, including an explanation of ideas related to Ligeti’s mathematical inspiration. Part II (Chapters 3-5) delves into an analysis of the rhythm, form, melody / motive, and harmony. Appendix A is a reduced score of the entire movement, labeled according to my analysis.

Computing The Optimal Path In Stochastic Dynamical Systems, 2016 Montclair State University

#### Computing The Optimal Path In Stochastic Dynamical Systems, Martha Bauver, Eric Forgoston, Lora Billings

##### Department of Mathematical Sciences Faculty Scholarship and Creative Works

In stochastic systems, one is often interested in finding the optimal path that maximizes the probability of escape from a metastable state or of switching between metastable states. Even for simple systems, it may be impossible to find an analytic form of the optimal path, and in high- dimensional systems, this is almost always the case. In this article, we formulate a constructive methodology that is used to compute the optimal path numerically. The method utilizes finite-time Lyapunov exponents, statistical selection criteria, and a Newton-based iterative minimizing scheme. The method is applied to four examples. The first example is a ...

Computing The Optimal Path In Stochastic Dynamical Systems, 2016 Montclair State University

#### Computing The Optimal Path In Stochastic Dynamical Systems, Martha Bauver, Eric Forgoston, Lora Billings

##### Lora Billings

In stochastic systems, one is often interested in finding the optimal path that maximizes the probability of escape from a metastable state or of switching between metastable states. Even for simple systems, it may be impossible to find an analytic form of the optimal path, and in high- dimensional systems, this is almost always the case. In this article, we formulate a constructive methodology that is used to compute the optimal path numerically. The method utilizes finite-time Lyapunov exponents, statistical selection criteria, and a Newton-based iterative minimizing scheme. The method is applied to four examples. The first example is a ...

Anthrax Models Involving Immunology, Epidemiology And Controls, 2016 University of Tennessee, Knoxville

#### Anthrax Models Involving Immunology, Epidemiology And Controls, Buddhi Raj Pantha

##### Doctoral Dissertations

This dissertation is divided in two parts. Chapters 2 and 3 consider the use of optimal control theory in an anthrax epidemiological model. Models consisting system of ordinary differential equations (ODEs) and partial differential differential equations (PDEs) are considered to describe the dynamics of infection spread. Two controls, vaccination and disposal of infected carcasses, are considered and their optimal management strategies are investigated. Chapter 4 consists modeling early host pathogen interaction in an inhalational anthrax infection which consists a system of ODEs that describes early dynamics of bacteria-phagocytic cell interaction associated to an inhalational anthrax infection.

First we consider a ...

Open And Dense Topological Transitivity Of Extensions By Non-Compact Fiber Of Hyperbolic Systems: A Review, 2016 West Chester University of Pennsylvania

#### Open And Dense Topological Transitivity Of Extensions By Non-Compact Fiber Of Hyperbolic Systems: A Review, Viorel Nitica, Andrei Török

##### Viorel Nitica

Currently, there is great renewed interest in proving the topological transitivity of various classes of continuous dynamical systems. Even though this is one of the most basic dynamical properties that can be investigated, the tools used by various authors are quite diverse and are strongly related to the class of dynamical systems under consideration. The goal of this review article is to present the state of the art for the class of Hölder extensions of hyperbolic systems with non-compact connected Lie group fiber. The hyperbolic systems we consider are mostly discrete time. In particular, we address the stability and genericity ...

Open And Dense Topological Transitivity Of Extensions By Non-Compact Fiber Of Hyperbolic Systems: A Review, 2016 West Chester University of Pennsylvania

#### Open And Dense Topological Transitivity Of Extensions By Non-Compact Fiber Of Hyperbolic Systems: A Review, Viorel Nitica, Andrei Török

##### Viorel Nitica

Currently, there is great renewed interest in proving the topological transitivity of various classes of continuous dynamical systems. Even though this is one of the most basic dynamical properties that can be investigated, the tools used by various authors are quite diverse and are strongly related to the class of dynamical systems under consideration. The goal of this review article is to present the state of the art for the class of Hölder extensions of hyperbolic systems with non-compact connected Lie group fiber. The hyperbolic systems we consider are mostly discrete time. In particular, we address the stability and genericity ...