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# Non-linear Dynamics Commons™

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524 Full-Text Articles 521 Authors 161,491 Downloads 64 Institutions

## All Articles in Non-linear Dynamics

524 full-text articles. Page 6 of 20.

2017 State University of New York at New Paltz

#### Balanced Excitation And Inhibition Shapes The Dynamics Of A Neuronal Network For Movement And Reward, Anca R. Radulescu

##### Biology and Medicine Through Mathematics Conference

No abstract provided.

Applying Fmri Complexity Analyses To The Single-Subject: A Case Study For Proposed Neurodiagnostics, 2017 State University of New York at New Paltz

#### Applying Fmri Complexity Analyses To The Single-Subject: A Case Study For Proposed Neurodiagnostics, Anca R. Radulescu, Emily R. Hannon

##### Biology and Medicine Through Mathematics Conference

No abstract provided.

2017 Loyola Marymount University

#### Comparison Of The Regulatory Dynamics Of Related Small Gene Regulatory Networks That Control The Response To Cold Shock In Saccharomyces Cerevisiae, Natalie Williams

##### Honors Thesis

The Dahlquist Lab investigates the global, transcriptional response of Sacchromyces cerevisiae, baker’s yeast, to the environmental stress of cold shock, using DNA microarrays for the wild type strain and strains deleted for a particular regulatory transcription factor. Gene regulatory networks (GRNs) consist of transcription factors (TF), genes, and the regulatory connections between them that control the resulting mRNA and protein expression levels. We use mathematical modeling to determine the dynamics of the GRN controlling the cold shock response to determine the relative influence of each transcription factor in the network. A family of GRNs has been derived from the ...

Application Of Symplectic Integration On A Dynamical System, 2017 East Tennessee State University

#### Application Of Symplectic Integration On A Dynamical System, William Frazier

##### Electronic Theses and Dissertations

Molecular Dynamics (MD) is the numerical simulation of a large system of interacting molecules, and one of the key components of a MD simulation is the numerical estimation of the solutions to a system of nonlinear differential equations. Such systems are very sensitive to discretization and round-off error, and correspondingly, standard techniques such as Runge-Kutta methods can lead to poor results. However, MD systems are conservative, which means that we can use Hamiltonian mechanics and symplectic transformations (also known as canonical transformations) in analyzing and approximating solutions. This is standard in MD applications, leading to numerical techniques known as symplectic ...

2017 Georgia State University

#### Comparing Methods Of Measuring Chaos In The Symbolic Dynamics Of Strange Attractors, James J. Scully

##### Georgia State Undergraduate Research Conference

No abstract provided.

2017 College of William and Mary

#### Center Manifold Theory And Computation Using A Forward Backward Approach, Emily E. Schaal

##### Undergraduate Honors Theses

The center manifold, an object from the field of differential equations, is useful in describing the long time behavior of the system. The most common way of computing the center manifold is by using a Taylor approximation. A different approach is to use iterative methods, as presented in Fuming and Kupper, 1994, Dellnitz and Hohmann, 1997, and Jolly and Rosa, 2005. In particular, Jolly and Rosa present a method based on a discretization of the Lyapunov-Perron (L-P) operator. One drawback is that this discretization can be expensive to compute and have error terms that are difficult to control. Using a ...

Classification Of Rectifying Space-Like Submanifolds In Pseudo-Euclidean Spaces, 2017 Michigan State University

#### Classification Of Rectifying Space-Like Submanifolds In Pseudo-Euclidean Spaces, Bang Yen Chan, Yun Myung Oh

##### Faculty Publications

The notions of rectifying subspaces and of rectifying submanifolds were introduced in [B.-Y. Chen, Int. Electron. J. Geom 9 (2016), no. 2, 1–8]. More precisely, a submanifold in a Euclidean m-space Em is called a rectifying submanifold if its position vector field always lies in its rectifying subspace. Several fundamental properties and classification of rectifying submanifolds in Euclidean space were obtained in [B.-Y. Chen, op. cit.]. In this present article, we extend the results in [B.-Y. Chen, op. cit.] to rectifying space- like submanifolds in a pseudo-Euclidean space with arbitrary codimension. In particular, we completely classify ...

P26. Global Exponential Stabilization On So(3), 2017 sberkane@uwo.ca

#### P26. Global Exponential Stabilization On So(3), Soulaimane Berkane

##### Western Research Forum

Global Exponential Stabilization on SO(3)

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

#### A Physics-Based Approach To Modeling Wildland Fire Spread Through Porous Fuel Beds, Tingting Tang

##### Theses and Dissertations--Mechanical Engineering

Wildfires are becoming increasingly erratic nowadays at least in part because of climate change. CFD (computational fluid dynamics)-based models with the potential of simulating extreme behaviors are gaining increasing attention as a means to predict such behavior in order to aid firefighting efforts. This dissertation describes a wildfire model based on the current understanding of wildfire physics. The model includes physics of turbulence, inhomogeneous porous fuel beds, heat release, ignition, and firebrands. A discrete dynamical system for flow in porous media is derived and incorporated into the subgrid-scale model for synthetic-velocity large-eddy simulation (LES), and a general porosity-permeability model ...

Neutrosophic Operational Research - Vol. 2, 2017 University of New Mexico

#### Neutrosophic Operational Research - Vol. 2, Florentin Smarandache, Mohamed Abdel Basset, Victor Chang

##### Mathematics and Statistics Faculty and Staff Publications

Foreword John R. Edwards This book is an excellent exposition of the use of Data Envelopment Analysis (DEA) to generate data analytic insights to make evidence-based decisions, to improve productivity, and to manage cost-risk and benefitopportunity in public and private sectors. The design and the content of the book make it an up-to-date and timely reference for professionals, academics, students, and employees, in particular those involved in strategic and operational decisionmaking processes to evaluate and prioritize alternatives to boost productivity growth, to optimize the efficiency of resource utilization, and to maximize the effectiveness of outputs and impacts to stakeholders. It ...

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 $V=0$.

2017 University of Kentucky

#### Autonomous Quadrotor Collision Avoidance And Destination Seeking In A Gps-Denied Environment, Thomas C. Kirven

##### Theses and Dissertations--Mechanical Engineering

This thesis presents a real-time autonomous guidance and control method for a quadrotor in a GPS-denied environment. The quadrotor autonomously seeks a destination while it avoids obstacles whose shape and position are initially unknown. We implement the obstacle avoidance and destination seeking methods using off-the-shelf sensors, including a vision-sensing camera. The vision-sensing camera detects the positions of points on the surface of obstacles. We use this obstacle position data and a potential-field method to generate velocity commands. We present a backstepping controller that uses the velocity commands to generate the quadrotor's control inputs. In indoor experiments, we demonstrate that ...

2017 Technological University Dublin

#### Hamiltonian Model For Coupled Surface And Internal Waves In The Presence Of Currents, Rossen Ivanov

##### Articles

We examine a two dimensional fluid system consisting of a lower medium bounded underneath by a flatbed and an upper medium with a free surface. The two media are separated by a free common interface. The gravity driven surface and internal water waves (at the common interface between the media) in the presence of a depth-dependent current are studied under certain physical assumptions. Both media are considered incompressible and with prescribed vorticities. Using the Hamiltonian approach the Hamiltonian of the system is constructed in terms of ’wave’ variables and the equations of motion are calculated. The resultant equations of motion ...

Region Of Smooth Functions For Positive Solutions To An Elliptic Biological Model, 2017 Andrews University

#### Region Of Smooth Functions For Positive Solutions To An Elliptic Biological Model, Joon Hyuk Kang, Timothy Robertson

##### Faculty Publications

The non-existence and existence of the positive solution to the generalized elliptic model ∆u+g(u v) = 0 in Ω, ∆v+h(u, v) = 0 in Ω, u=v= 0 on∂Ω, were investigated.

2016 University of Louisville

#### Spreading Speeds Along Shifting Resource Gradients In Reaction-Diffusion Models And Lattice Differential Equations., Jin Shang

##### Electronic Theses and Dissertations

A reaction-diffusion model and a lattice differential equation are introduced to describe the persistence and spread of a species along a shifting habitat gradient. The species is assumed to grow everywhere in space and its growth rate is assumed to be monotone and positive along the habitat region. We show that the persistence and spreading dynamics of a species are dependent on the speed of the shifting edge of the favorable habitat, c, as well as c*(∞) and c*(−∞), which are formulated in terms of the dispersal kernel and species growth rates in both directions. When the favorable habitat edge ...

2016 College of William and Mary

#### (Un)Stable Manifold Computation Via Iterative Forward-Backward Runge-Kutta Type Methods, Dmitriy Zhigunov

##### Undergraduate Honors Theses

I present numerical methods for the computation of stable and unstable manifolds in autonomous dynamical systems. Through differentiation of the Lyapunov-Perron operator in [Casteneda, Rosa 1996], we find that the stable and unstable manifolds are boundary value problems on the original set of differential equation. This allows us to create a forward-backward approach for manifold computation, where we iteratively integrate one set of variables forward in time, and one set of variables backward in time. Error and stability of these methods is discussed.

2016 University of Massachusetts Amherst

#### Studies On Lattice Systems Motivated By Pt-Symmetry And Granular Crystals, Haitao Xu

##### Doctoral Dissertations

This dissertation aims to study some nonlinear lattice dynamical systems arising in various areas, especially in nonlinear optics and in granular crystals. At first, we study the 2-dimensional PT-symmetric square lattices (of the discrete non-linear Schr¨odinger (dNLS) type) and identify the existence, stability and dynamical evolu- tion of stationary states, including discrete solitons and vortex configurations. To enable the analytical study, we consider the so-called anti-continuum (AC) limit of lattices with uncoupled sites and apply the Lyapunov–Schmidt reduction. Numerical experiments will also be provided accordingly. Secondly, we investigate the nonlinear waves in the granular chains of elastically inter- ...

Stability Analysis Of A Prey Refuge Predator-Prey Model With Allee Effects, 2016 American University of the Middle East

#### Stability Analysis Of A Prey Refuge Predator-Prey Model With Allee Effects, Unal Ufuktepe Prof

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

No abstract provided.