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# Dynamical Systems Commons™

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242 Full-Text Articles 320 Authors 51,457 Downloads 44 Institutions

## All Articles in Dynamical Systems

242 full-text articles. Page 2 of 11.

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 $V=0$.

Renewable Energy And Sustainable Development (Resd) Group, 2016 Wroclaw University of Technology

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

##### Wojciech Budzianowski

No abstract provided.

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

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

##### Wojciech Budzianowski

No abstract provided.

C.V. - Wojciech Budzianowski, 2016 Wojciech Budzianowski Consulting Services

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

##### Wojciech Budzianowski

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Dynamic Testing Of Wholesale Power Market Designs: An Open-Source Agent-Based Framework, 2016 Iowa State University

#### Dynamic Testing Of Wholesale Power Market Designs: An Open-Source Agent-Based Framework, Junjie Sun, Leigh Tesfatsion

##### Leigh Tesfatsion

In April 2003 the U.S. Federal Energy Regulatory Commission proposed a complicated market design – the Wholesale Power Market Platform (WPMP) – for common adoption by all U.S. wholesale power markets. Versions of the WPMP have been implemented in New England, New York, the mid-Atlantic states, the Midwest, the Southwest, and California. Strong opposition to the WPMP persists among some industry stakeholders, however, due largely to a perceived lack of adequate performance testing. This study reports on the model development and open-source implementation (in Java) of a computational wholesale power market organized in accordance with core WPMP features and operating ...

Dynamic Testing Of Wholesale Power Market Designs: An Open-Source Agent-Based Framework, 2016 United States Treasury

#### Dynamic Testing Of Wholesale Power Market Designs: An Open-Source Agent-Based Framework, Junjie Sun, Leigh Tesfatsion

##### Leigh Tesfatsion

In April 2003 the U.S. Federal Energy Regulatory Commission proposed a complicated market design—the Wholesale Power Market Platform (WPMP)—for common adoption by all US wholesale power markets. Versions of the WPMP have been implemented in New England, New York, the mid-Atlantic states, the Midwest, the Southwest, and California. Strong opposition to the WPMP persists among some industry stakeholders, however, due largely to a perceived lack of adequate performance testing. This study reports on the model development and open-source implementation (in Java) of a computational wholesale power market organized in accordance with core WPMP features and operating over ...

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.

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 ...

Geometrical Models For Grain Dynamics, 2016 Universidade Federal de Pernambuco

#### Geometrical Models For Grain Dynamics, Giovani L. Vasconcelos, J. J. P. Veerman

##### J. J. P. Veerman

We study models for the gravity-driven, dissipative motion of a single grain on an inclined rough surface. Imposing some conditions on the momentum loss due to the collisions between the particle and the surface, we arrive at a class of models in which the grain dynamics is described by one-dimensional maps. The dynamics of these maps is studied in detail. We prove the existence of various dynamical phases and show that the presence of these phases is independent of the restitution law (within the class considered).

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 ...

Signal Velocity In Oscillator Arrays, 2016 Portland State University

#### Signal Velocity In Oscillator Arrays, Carlos E. Cantos, J.J. P. Veerman, David K. Hammond

##### J. J. P. Veerman

We investigate a system of coupled oscillators on the circle, which arises from a simple model for behavior of large numbers of autonomous vehicles. The model considers asymmetric, linear, decentralized dynamics, where the acceleration of each vehicle depends on the relative positions and velocities between itself and a set of local neighbors. We first derive necessary and sufficient conditions for asymptotic stability, then derive expressions for the phase velocity of propagation of disturbances in velocity through this system. We show that the high frequencies exhibit damping, which implies existence of well-defined signal velocities c+>0 and c−f(x−c ...

Full State Revivals In Linearly Coupled Chains With Commensurate Eigenspectra, 2016 Portland State University

#### Full State Revivals In Linearly Coupled Chains With Commensurate Eigenspectra, J. J. P. Veerman, Jovan Petrovic

##### J. J. P. Veerman

Coherent state transfer is an important requirement in the construction of quantum computer hardware. The state transfer can be realized by linear next-neighbour-coupled finite chains. Starting from the commensurability of chain eigenvalues as the general condition of periodic dynamics, we find chains that support full periodic state revivals. For short chains, exact solutions are found analytically by solving the inverse eigenvalue problem to obtain the coupling coefficients between chain elements. We apply the solutions to design optical waveguide arrays and perform numerical simulations of light propagation thorough realistic waveguide structures. Applications of the presented method to the realization of a ...

On Rank Driven Dynamical Systems, 2016 Portland State University

#### On Rank Driven Dynamical Systems, J. J. P. Veerman, F. J. Prieto

##### J. J. P. Veerman

We investigate a class of models related to the Bak-Sneppen model, initially proposed to study evolution. The BS model is extremely simple and yet captures some forms of “complex behavior” such as self-organized criticality that is often observed in physical and biological systems. In this model, random fitnesses in [0, 1] are associated to agents located at the vertices of a graph G. Their fitnesses are ranked from worst (0) to best (1). At every time-step the agent with the worst fitness and some others with a priori given rank probabilities are replaced by new agents with random fitnesses. We ...

An Expansion Property Of Boolean Linear Maps, 2016 Shanghai Jiao Tong University

#### An Expansion Property Of Boolean Linear Maps, Yaokun Wu, Zeying Xu, Yinfeng Zhu

##### Electronic Journal of Linear Algebra

Given a finite set $K$, a Boolean linear map on $K$ is a map $f$ from the set $2^K$ of all subsets of $K$ into itself with $f(\emptyset )=\emptyset$ such that $f(A\cup B)=f(A)\cup f(B)$ holds for all $A,B\in 2^K$. For fixed subsets $X, Y$ of $K$, to predict if $Y$ is reachable from $X$ in the dynamical system driven by $f$, one can assume the existence of nonnegative integers $h$ with $f^h(X)=Y$, find an upper bound $\alpha$ for the minimum of all such assumed integers \$h ...