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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 p
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 x
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 Yoshizaw
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 poss
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
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
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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
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 )x