2.050J/12.006J/18.353J
Nonlinear
Dynamics
I:
Chaos,
Fall
2012
Problem
Set
4
Due
at
12:01
pm
on
Friday,
October
5th,
in
the
box
provided.
No
late
psets
are
accepted.
If
you
collaborated
with
other
students
in
the
class,
list
their
names
on
the
title
sheet.
The
work
that
you
submit
must
be
your
own.
Main
concepts:
Three
bifurcations
in
1D
dynamical
systems
(saddle-node,
transcritical,
and
pitchfork).
Reading:
Strogatz
Ch.
3.
Problem
1:
Bifurcations
of
1D
dynamical
systems.
Normal
forms.
For
each
of
the
following
problems,
•
sketch
all
the
qualitatively
different
vector
fields
that
occur
as
r
is
varied.
•
Find
at
which
x
and
for
which
critical
values
of
the
parameter
r
the
bifurcation
occurs.
•
Which
bifurcation
is
it
(saddle-node,
transcritical,
supercritical
pitchfork,
or
subcritical
pitchfork)?
∗
•
Finally,
sketch
or
plot
in
MATLAB
the
bifurcation
diagram
of
fixed
points
x
versus
r
,
and
mark
the
stable
branches
as
solid
lines,
while
the
unstable
branches
as
dashed
lines.
(Note:
for
some
of
the
cases
it
is
simpler
to
plot
the
bifurcation
in
MATLAB).
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- Fall '12
- LyubovChumakova
- Sets, Bifurcation, Bifurcation theory, 1D dynamical systems
