Modelling Lab 2: Arrays, Loops, and
Random Numbers
Lab 2: Learning Objectives
In this lab you will learn about a basic data structure (arrays) and a simple looping
structure (for loop) that are commonlyused in MATLAB; you will use these structures
to ana
Lab 7 (Oct 31): Coupled differential
equations
Math 360
2013W1
Note: this lab is due Tuesday, Nov 5, 5 pm.
In this lab, we study the dynamics in systems of two coupled differential equations using Matlabs numerical differential equation solver. Numerical
Modelling Lab 3: Discrete Time Series
Lab 3: Learning Objectives
In this lab you will learn how to generate and plot a discrete time series for a given
dynamical system using MATLAB. You will also think about how to interpret discretetime dynamical system
Reading assignment for quiz on
Thursday, Sept 26
Math 360
Term 1, Winter 2013
In this assignment you should familiarize yourself with the technique of cobwebbing introduced in class, as follows. Consider the dynamical system
x(t + 1) = F (x(t) = r x(t) (1
Lab 5 (Oct 8): Stability analysis and
Stochastic discrete time series
Math 360
2013W1
Part 1: Stability analysis
Consider the following discrete time dynamical system:
x(t + 1) =
x
.
1 + axb
(1)
Assume that > 1. Determine all equilibria of the dynamical s
Lab 4 (Oct 1): Bifurcation diagrams for
discretetime dynamical systems
Math 360
2013W/1
1. Many insect species have an annual life cycle that can be described as follows.
Each year, individuals that arepresent at the beginning of the year rst undergo
a p
Lab 8 (Nov 12): Stochastic evolution in
nite populations
Math 360
2013W1
1. Consider the RockPaperScissor game given by the following payoff matrix:
Rock Paper Scissor
Rock
0
1
1
Paper
1
0
1
Scissor
1
1
0
a) Argue that there is no ESS (evolutonarily sta
Lab 6 (Oct 24): Formulating differential
equations based on individual reactions
and solving differential equations with
Matlab
Math 360
2013W1
Note: The deadline for this lab is Tuesday, Oct 29, 5 pm.
1. Consider the differential equation
dn
= t n(t),
(1
Lab 9 (Nov 28): Stochastic evolution in
nite populations
Math 360
2013W1
This lab is due on Tuesday, December 3.
In this lab, we use the whilecommand to iterate a stochastic system until a certain
condition is satised. We consider a nite population of N
Review of Math 360, Fall 2013
Below are, very briey, the main topics covered in the course. You should be familiar
with these topics for the nal exams. You should also be familiar with the methods
used in the lab projects throughout the course.
1. Optimiz
Midterm exam I, October 15, 2013
Math 360
2013W1
Notes:
 This is an open book exam. You may consult course notes and lab projects
to answer the questions. You may also consult the web (however, it is unlikely
that this will be of immediate help).
 You m
Final exam I, November 19, 2013
Math 360
2013W1
Notes:
 This is an open book exam. You may consult course notes and lab projects
to answer the questions. You may also consult the web (however, it is unlikely
that this will be of immediate help).
 You ma
Midterm exam II, October 17, 2013
Math 360
2013W1
Notes:
 This is an open book exam. You may consult course notes and lab projects
to answer the questions. You may also consult the web (however, it is unlikely
that this will be of immediate help).
 Each
Modelling Lab 1: Introduction to MATLAB
and A Simple Optimization Problem
Welcome to the computing component of MATH 360. Every Tuesday throughout the term
you will be working on a small modelling project; we strongly recommend that you make use
of comput
Final exam II, November 21, 2013
Math 360
2013W1
Notes:
 This is an open book exam. You may consult course notes and lab projects
to answer the questions. You may also consult the web (however, it is unlikely
that this will be of immediate help).
 You m
.,.
9
r
C
e
U
&
&
c
Q
3

C
7
<4
7
52
4

fl
C
V
p.
1]
4

+
9:
N
.
r
r
C
C
t
I

7
,
I
C
C
C
r
C
2
r
n
5
c
L
*
a
1%
4
r
7
c
.
V.
C
2
s
t
F
N
V

ONI,
.
Li
fl
cp
C
5
a
C
?
+
N
Ii
N)
S
N
4
c.
1
S
Ni)
is
LI
C
S
S
C)
LI
f
*4
L_J
$
N
C