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Solutions manual for de Vries et al, SIAM 2006
1.4
Exercises for Modeling
Exercise 1.4.1: Discrete-time versus continuous-time models
(a) t = 10 minutes, and the probability of one cell making one other cell in 10
minu
Completing the square
The basic idea here is we want to take an expression of the form
a1 x 2 + a2 x + a3 = 0
and rewrite it as
a1 (x + b2 )2 + b3 = 0
Method 1:
In other words, we want to express a1 x2 +a2 x+a3 in the form a1 (x+b2 )2 +b3 .
We can determi
Math 371 Assignment 3: Partial Dierential Equations
Due March 25, 2010
This problem set is concerned with a model for signal transduction in the
axon proposed by Fitzhugh, Nagumo, Arimoto and Yoshizawa (see Exercise
4.5.5 in the text).
Let u be the membra
Bifurcation theory for discrete time systems
Saddle node bifurcation
Normal form:
xt+1 = xt + x2
t
In general, a saddle node bifurcation occurs if, near the bifurcation point
(xc , c ), the model possesses a unique curve of xed points in the (x, ) plane
w
Math 371 Assignment 2: Ordinary Dierential
Equations
Due March 9, 2010
This problem set is concerned with an epidemic model called the KermackMcKendrick model.
Suppose there are three compartments in the population:
S(t) - Susceptibles
I(t) - Infective
R(
Math 371 Assignment 1: Discrete Time models
Due February 4, 2010
This problem set is concerned with a host-parasitoid model called the
Nicholson-Bailey model.
Suppose we make the following assumptions
1. Hosts that have been parasitized give rise to the n
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A. Beltaos, G. de Vries, T. Hillen, November 20, 2006
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qualitative sketch of bifurcation diagram
3
2.5
x
2
1.5
1
0.5
0
X: 0.04183
Y: 0.2198
0
0.05
0.1
0.15
s
0.2
0.25
0.3
Exercise 3.9.7: Linear systems
Thanks to Pando
Math 371 Midterm Exam Solutions
1. Consider the nonlinear equation for population growth
xn+1 =
xn
1 + xn
with > 0
(a) Recall the net per capita growth rate is the function g(xn ) where
xn+1 = g(xn )xn . Plot the net per capita growth rate and give a
biol