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Dynamical Systems Commons

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Full-Text Articles in Dynamical Systems

Mechanical Visualization Of A Second Order Dynamic Equation On Varying Time Scales, Molly Kathryn Peterson Jan 2014

Mechanical Visualization Of A Second Order Dynamic Equation On Varying Time Scales, Molly Kathryn Peterson

Theses, Dissertations and Capstones

In this work, we give an introduction to Time Scales Calculus, the properties of the exponential function on an arbitrary time scale, and use it to solve linear dynamic equation of second order. Time Scales Calculus was introduced by Stefan Hilger in 1988. It brings together the theories of difference and differential equations into one unified theory. By using the properties of the delta derivative and the delta anti-derivative, we analyze the behavior of a second order linear homogeneous dynamic equation on various time scales. After the analytical discussion, we will graphically evaluate the second order dynamic equation in Marshall’s …


Finding Positive Solutions Of Boundary Value Dynamic Equations On Time Scale, Olusegun Michael Otunuga Jan 2009

Finding Positive Solutions Of Boundary Value Dynamic Equations On Time Scale, Olusegun Michael Otunuga

Theses, Dissertations and Capstones

This thesis is on the study of dynamic equations on time scale. Most often, the derivatives and anti-derivatives of functions are taken on the domain of real numbers, which cannot be used to solve some models like insect populations that are continuous while in season and then follow a difference scheme with variable step-size. They die out in winter, while the eggs are incubating or dormant; and then they hatch in a new season, giving rise to a non overlapping population. The general idea of my thesis is to find the conditions for having a positive solution of any boundary …


Non-Preemptive Shunting In M/M/1 And Dynamic Service Queueing Systems, Steven Lacek Jan 2008

Non-Preemptive Shunting In M/M/1 And Dynamic Service Queueing Systems, Steven Lacek

Theses, Dissertations and Capstones

We provide a study of two queueing systems, namely, an M/M/1 queueing system in which an incoming customer shunts, or skips line, and a dynamic server in an infinite capacity system moving among service nodes. In the former, we explore various aspects of the system, including waiting time, and the relationships between shunting and position in queue and rate of service. Through use of global balance equations, we find the probability that an arriving non-priority customer, finding customers waiting in the system, will shunt to a position other than behind the queue. In the latter, we explore a system in …


The Dynamics Of Newton's Method On Cubic Polynomials, Shannon N. Miller Jan 2006

The Dynamics Of Newton's Method On Cubic Polynomials, Shannon N. Miller

Theses, Dissertations and Capstones

The field of dynamics is itself a huge part of many branches of science, including the motion of the planets and galaxies, changing weather patterns, and the growth and decline of populations. Consider a function f and pick x0 in the domain of f . If we iterate this function around the point x0, then we will have the sequence x0, f (x0), f (f (x0)), f (f (f (x0))), ..., which becomes our dynamical system. We are essentially interested in the end behavior of this system. Do …