Kenyon College
Dana Paquin
[email protected]
The Traveling Salesman Problem.
Given a graph with n vertices, having an edge between every pair of vertices, what
is the shortest cycle which starts at a particular vertex, visits every other vertex
exactly o
Kenyon College
Dana Paquin
[email protected]
Math 347
Due Thursday, November 1, 2007.
Note: You will need the result from Problem 2 to complete Discrete Dynamical
Systems Homework 3.
Solutions of linear and ane dynamical systems
Denition. The general sol
Kenyon College
Dana Paquin
[email protected]
Math 347
Discrete Dynamical Systems Homework 4
Due Tuesday, November 6, 2007
The cobweb theorem of economics. In this series of exercises, we will develop
a discrete dynamical system to model supply and demand
Kenyon College
Dana Paquin
[email protected]
Math 347
Discrete Dynamical Systems Homework 3
Due Thursday, November 1, 2007
A model of an arms race. We will develop a model of a two-nation arms race. A
variation of this model was originally developed by L
Kenyon College
Dana Paquin
[email protected]
Math 347
Discrete Dynamical Systems Homework 2
Due Tuesday, October 30, 2007
1. Consider the dynamical system
A(n + 1) = 2A(n) 0.25A2 (n) 0.75.
Show that the two equilibrium values of this system are a = 1 and
Kenyon College
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Math 347
Discrete Dynamical Systems of Several Equations
Example. Consider the following study of population growth. Consider a species
which can be broken into three equal age groups: 0-1 years, 1-2 years, and 2-3
years.
Kenyon College
Dana Paquin
[email protected]
Math 347
Euler Cycles Problems
1. Suppose that a new articial island were placed in the Pregel River in between
islands B and C . If the bridge from B to C is removed and several bridges built
connecting the n
Kenyon College
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Math 347
Thursday, November 8, 2007
Chaos and the Lorenz Equations
Does the ap of a butterys wings in Brazil set o a tornado in Texas?
These problems are due on Thursday, November 15, 2007.
1. Consider a layer of air that
Kenyon College
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Math 347
Tuesday, October 16, 2007
Lotka-Volterra Predator-Prey Model
So far, we have considered competing species models in which two competing species live in the
same environment and compete for food and other ecologic
Kenyon College
Dana Paquin
[email protected]
Math 347
Homework 7: Continuous Dynamical Systems
Due Thursday, October 18, 2007
Note: We will discuss Problems 2 and 3 in class on Tuesday. Please think about the
problems over the weekend, and be prepared to
Kenyon College
Dana Paquin
[email protected]
Math 347
Hamilton Cycles Problems
1. Construct a graph with a Hamilton cycle but no Euler cycle.
2. Construct a graph with an Euler cycle but no Hamilton cycle.
3. Determine which of the following graphs are H
Kenyon College
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Math 347
Discrete Dynamical Systems Homework 1
Note: These problems are due on Thursday, October 25.
1. Consider the discrete dynamical system
A(n + 1) = 0.8A(n) 2.
Find the equilibrium value (if one exists) of the system