Susanna Mostaghim
MATH 4454
Homework 1
1. Lab 1
1. Consider the logistic model:
x(n + 1) = rx(n)(1 x(n)
Find the behavior of the system for
i. x(0) = 0.3, r = 0.5, n = 100
The behavior of this system is decreasing exponentially and x 0 as t . It converges

Math 4454- Homework 3- due March 1st in class
1. For the following system, determine the conditions on the parameter a such that the origin is (i) saddle; (ii)
stable node; (iii) stable spiral.
dx
= (a 1)x + y,
dt
dy
= x + y.
dt
2. A model of population g

MATH 4424
Spring 2016
Principals of Mathematical Modeling
1. What is it?
Def: A formulation in mathematical terms of the assumptions believed to underline a particular real world
problem
Ex
(a) Newtons 2nd law
F=
d
2
(m~v) = m 2
dt
t
(b) x = population, r

Math 4454- Homework 4 - due March 31th during class
1. Complete and submit Lab 3.
2. Consider the cooperative phenomena model where one enzyme has two binding sites given by
k2
1+
S+E
E + P
C1
k
k
1
k3+
k4
S + C1
C1 + P
C2
k
3
with initial conditio