# Dynamical Systems Commons™

## All Articles in Dynamical Systems

253 full-text articles. Page 4 of 11.

An Inverse Eigenproblem For Generalized Reflexive Matrices With Normal $K+1$-Potencies, 2016 East China Normal University

#### An Inverse Eigenproblem For Generalized Reflexive Matrices With Normal $K+1$-Potencies, Wei-Ru Xu, Guo-Liang Chen

##### Electronic Journal of Linear Algebra

Let $P,~Q\in\mathbb{C}^{n\times n}$ be two normal $\{k+1\}$-potent matrices, i.e., $PP^{*}=P^{*}P,~P^{k+1}=P$, $QQ^{*}=Q^{*}Q,~Q^{k+1}=Q$, $k\in\mathbb{N}$. A matrix $A\in\mathbb{C}^{n\times n}$ is referred to as generalized reflexive with two normal $\{k+1\}$-potent matrices $P$ and $Q$ if and only if $A=PAQ$. The set of all $n\times n$ generalized reflexive matrices which rely on the matrices $P$ and $Q$ is denoted by $\mathcal{GR}^{n\times n}(P,Q)$. The left and right inverse ...

Geometric Limits Of Julia Sets Of Maps Z^N + Exp(2Πiθ) As N → ∞, 2016 Butler University

#### Geometric Limits Of Julia Sets Of Maps Z^N + Exp(2Πiθ) As N → ∞, Scott Kaschner, Reaper Romero, David Simmons

##### Scott Kaschner

We show that the geometric limit as n → ∞ of the Julia sets J(Pn,c) for the maps Pn,c(z) = zn + c does not exist for almost every c on the unit circle. Furthermore, we show that there is always a subsequence along which the limit does exist and equals the unit circle.

Rational Map Of Cp^2 With No Invariant Foliation, 2016 Butler University

#### Rational Map Of Cp^2 With No Invariant Foliation, Scott Kaschner, Rodrigo Perez, Roland Roeder

##### Scott Kaschner

Conference Poster presented at: Midwest Dynamical Systems Conference, Champaign/Urbana, IL November 1-3, 2013.

Elements Of Dynamic Economic Modeling: Presentation And Analysis, 2016 Iowa State University

#### Elements Of Dynamic Economic Modeling: Presentation And Analysis, Leigh Tesfatsion

##### Economics Working Papers (2002–2016)

The primary goal of these introductory notes is to promote the clear presentation and rigorous analysis of dynamic economic models, whether expressed in equation or agent-based form. A secondary goal is to promote the use of state-space modeling with its respect for historical process, for cause leading to effect without top-down imposition of global constraints. If economic modelers truly wish to respect the rationality of decision-makers, they should have the courage of their convictions; they should not be doing for their modeled decision-makers what in reality these decision-makers must do for themselves.

Movement Path Tortuosity In Free Ambulation: Relationships To Age And Brain Disease, 2016 University of South Florida

#### Movement Path Tortuosity In Free Ambulation: Relationships To Age And Brain Disease, William Kearns, James Fozard, Vilis Nams

##### William D. Kearns, PhD

Ambulation is defined by duration, distance traversed, number and size of directional changes and the interval separating successive movement episodes; more complex measures of ambulation can be created by aggregating these features. This review article of published findings defines random changes in direction during movement as “movement path tortuosity”, and relates tortuosity to the understanding of cognitive impairments of persons of all ages. Path tortuosity is quantified by subjecting tracking data to fractal analysis, specifically Fractal Dimension (Fractal D), which ranges from a value of 1 when the movement path is perfectly straight to a value of 2 when the ...

Procesy Cieplne I Aparaty (Lab), 2016 Wroclaw University of Technology

#### Procesy Cieplne I Aparaty (Lab), Wojciech M. Budzianowski

##### Wojciech Budzianowski

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Inżynieria Chemiczna Lab., 2016 Wroclaw University of Technology

#### Inżynieria Chemiczna Lab., Wojciech M. Budzianowski

##### Wojciech Budzianowski

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2016 Marshall University

#### A Mechanical Investigation Of Second Order Homogeneous Dynamic Equations On A Time Scale, Jacob E. Fischer

##### Theses, Dissertations and Capstones

This thesis covers the basic aspects of time scale calculus, a branch of mathematics combining the theories of differential equations and difference equations. Using the properties of time scale calculus we analyze a second order homogeneous dynamic equation with constant coefficients, in particular, y ∆∆ − 1 6 y ∆ + 1 8 y = 0. Following the analysis, this problem will be graphically evaluated using Marshall University’s Differential Analyzer, affectionately named Art. A differential analyzer is a machine that mechanically integrates by way of related rates of rotating rods. The process for making the jump between intervals on a time scale will be ...

Tridiagonal Matrices And Boundary Conditions, 2016 Portland State University

#### Tridiagonal Matrices And Boundary Conditions, J. J. P. Veerman, David K. Hammond

##### Mathematics and Statistics Faculty Publications and Presentations

We describe the spectra of certain tridiagonal matrices arising from differential equations commonly used for modeling flocking behavior. In particular we consider systems resulting from allowing an arbitrary boundary condition for the end of a one-dimensional flock. We apply our results to demonstrate how asymptotic stability for consensus and flocking systems depends on the imposed boundary condition.

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

##### Mathematics and Statistics Faculty Publications and Presentations

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 ...

Signal Velocity In Oscillator Arrays, 2016 Portland State University

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

##### Mathematics and Statistics Faculty Publications and Presentations

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 ...

2016 Harvey Mudd College

#### Topological Data Analysis For Systems Of Coupled Oscillators, Alec Dunton

##### HMC Senior Theses

Coupled oscillators, such as groups of fireflies or clusters of neurons, are found throughout nature and are frequently modeled in the applied mathematics literature. Earlier work by Kuramoto, Strogatz, and others has led to a deep understanding of the emergent behavior of systems of such oscillators using traditional dynamical systems methods. In this project we outline the application of techniques from topological data analysis to understanding the dynamics of systems of coupled oscillators. This includes the examination of partitions, partial synchronization, and attractors. By looking for clustering in a data space consisting of the phase change of oscillators over a ...

2015 University of Nebraska Medical Center

#### Postural Responses To Perturbations Of The Vestibular System During Walking In Healthy Young And Older Adults, Jung Hung Chien

##### Theses & Dissertations

It has been shown that approximate one-third of US adults aged 40 years and older (69 million US citizens) have some type of vestibular problems. These declining abilities of the vestibular system affect quality of life. Difficulties in performing daily activities (dressing, bathing, getting in and out of the bed and etc.) have been highly correlated to loss of balance due to vestibular disorders. The exact number of people affected by vestibular disorders is still difficult to quantify. This might be because symptoms are difficult to describe and differences exist in the qualifying criteria within and across studies. Thus, it ...

Gait Transition Dynamics Are Modulated By Experimental Protocol, 2015 University of Connecticut - Storrs

#### Gait Transition Dynamics Are Modulated By Experimental Protocol, Mohammad Abdolvahab, Jason Gordon

No abstract provided.

A Posteriori Eigenvalue Error Estimation For The Schrödinger Operator With The Inverse Square Potential, 2015 Wayne State University

#### A Posteriori Eigenvalue Error Estimation For The Schrödinger Operator With The Inverse Square Potential, Hengguang Li, Jeffrey S. Ovall

##### Mathematics and Statistics Faculty Publications and Presentations

We develop an a posteriori error estimate of hierarchical type for Dirichlet eigenvalue problems of the form (−∆ + (c/r) 2 )ψ = λψ on bounded domains Ω, where r is the distance to the origin, which is assumed to be in Ω. This error estimate is proven to be asymptotically identical to the eigenvalue approximation error on a family of geometrically-graded meshes. Numerical experiments demonstrate this asymptotic exactness in practice.

Phase Dynamics Of Locset Control Methodology, 2015 University of Tennessee - Knoxville

#### Phase Dynamics Of Locset Control Methodology, Brendan Neschke

##### Masters Theses

Single-mode fiber amplifiers produce diffraction-limited beams very efficiently. Maximum beam intensity requires that an array of these amplifiers have their beams coherently combined at the target. Optical path differences and noise adversely affect beam quality. An existing closed loop phase control methodology, called the locking of optical coherence by single-detector electronic-frequency tagging (LOCSET), corrects phase errors in real time by electronically detecting path length differences and sending signals to lithium niobate phase adjusters. Broadening the line-width using “jitter” of the input signal can increase the output power of an individual amplifier by suppressing nonlinearity. The system dynamics of LOCSET are ...

2015 Purdue University

#### Investigating Synergy: Mathematical Models For The Coupled Dynamics Of Hiv And Hsv-2 And Other Endemic Diseases, Christina M Alvey

##### Open Access Dissertations

This dissertation presents epidemiological models that investigate synergy: synergy between HIV and HSV-2 or between humans and mosquitoes in a malaria study. Each of the three coupled disease models addresses different epidemiological questions with regard to gender or disease structure in the context of sexually-transmitted diseases (STDs), while the malaria model focuses on age-structure of the human population. ^ Mounting evidence indicates that HSV-2 infection may increase susceptibility to HIV infection and that co-infection may increase infectiousness. Accordingly, antiviral treatment of people with HSV-2 may mitigate the incidence of HIV in populations where both pathogens occur. To better understand the epidemiological ...

Thirty Years Of Turnstiles And Transport, 2015 University of Colorado Boulder

#### Thirty Years Of Turnstiles And Transport, James Meiss

##### Applied Mathematics Faculty Contributions

To characterize transport in a deterministic dynamical system is to compute exit time distributions from regions or transition time distributions between regions in phase space. This paper surveys the considerable progress on this problem over the past thirty years. Primary measures of transport for volume-preserving maps include the exiting and incoming fluxes to a region. For area-preserving maps, transport is impeded by curves formed from invariant manifolds that form partial barriers, e.g., stable and unstable manifolds bounding a resonance zone or cantori, the remnants of destroyed invariant tori. When the map is exact volume preserving, a Lagrangian differential form ...

Open And Dense Topological Transitivity Of Extensions By Non-Compact Fiber Of Hyperbolic Systems: A Review, 2015 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

##### Mathematics

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 ...

Sandpiles, Spanning Trees, And Plane Duality, 2015 Gettysburg College

#### Sandpiles, Spanning Trees, And Plane Duality, Melody Chan, Darren B. Glass, Matthew Macauley, David Perkinson, Caryn Werner, Qiaoyu Yang

##### Math Faculty Publications

Let G be a connected, loopless multigraph. The sandpile group of G is a finite abelian group associated to G whose order is equal to the number of spanning trees in G. Holroyd et al. used a dynamical process on graphs called rotor-routing to define a simply transitive action of the sandpile group of G on its set of spanning trees. Their definition depends on two pieces of auxiliary data: a choice of a ribbon graph structure on G, and a choice of a root vertex. Chan, Church, and Grochow showed that if G is a planar ribbon graph, it ...