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
Student no. (in ink)
Name (PRINT in ink)
MATH 360
Midterm Test
Marks
Allowed aid: one 8.500 1100 sheet (both sides) of notes.
1. In the fisheries model
[25]
dN
= rN
dt
N
1
EN,
K
0 N < ,
N (t) is the population of fish at time t, and r (intrinsic per capi
MATH 360
Homework Assignment 4
Due Tuesday, 2015 November 17, 9:30 a.m.
1. For the following maps xn+1 = f (xn ) (or x 7 f (x): i. find (analytically) all fixed
points in the indicated domain; ii. determine (where possible) their linearized stabilities; i
MATH 360
Homework Assignment 2
Due Thursday, 2015 October 15, 9:30 a.m.
1. Here is one more model of a fishery,
dN
N
= rN 1
dt
K
M
N
,
N +A
N 0,
where N (t) 0 is the number of individuals (fish) at time t, and where r [time1 ], K
[individuals], M [indivi
MATH 360
Homework Assignment 5 Solutions
2015 November 26
1. (a) We assumee that the coins can be distinguished from each other. There are two outcomes
(H, T ) and (T, H), each with probability
(0.65)(0.35) = (0.35)(0.65) = 0.2275
if the coins are tossed
MATH 360
Homework Assignment 3
Due Tuesday, 2015 November 3, 9:30 a.m.
1. Consider the chemical reaction mechanism (written in abbreviated form)
k
1
k2
2S + E
2P + E
C
k1
where S is the substrate, E is the enzyme, C is the (substrateenzyme) complex,
MATH 360
Homework Assignment 5
Due Thursday, 2015 November 26, 9:30 a.m.
1. (a) Two unfair coins have been made so that, for each coin, heads comes up 65% of
the time (and tails comes up the rest of the time). If the two coins are tossed
independently, wh
MATH 360
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MATH 360
Homework Assignment 1
Due Thursday, 2015 October 1, 9:30 a.m.
1. The equation
N
dN
= rN 1
H
dt
K
is a simple model of a fishery. In the absence of harvesting (H = 0), the population
N of fish grows according to the logistic equation. The effects
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
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
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
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
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 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
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
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
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 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 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 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
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
.,.
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