The bifurcation tag has no wiki summary.
2
votes
1answer
70 views
Possible ways to do stability analysis of non-linear, three-dimensional Differential Equations
For example Lorenz system,
$$
\frac{d}{dt}\begin{pmatrix}
x\\
y\\
z
\end{pmatrix}=\begin{pmatrix}
-\sigma & \sigma & 0\\
\rho & -1 & -x\\
y & 0 & -\beta
...
3
votes
0answers
23 views
Chaos without period doubling
I have been studying the Duffing oscillator rather intensively lately, mainly based on the theory in of the book by Guckenheimer and Holmes. From all that I have gathered, it seems that most dynamical ...
0
votes
0answers
11 views
Divergent limit cycle frequency along a hopf boundary
I am studying the linear stability of continuous system as a function of two parameters (a and b) and I observe that a hopf bifurcation with frequency w happens along the line described by f(a,b). ...
1
vote
1answer
47 views
Conditions for Saddle-Node Bifurcations
I am reading the book on Chaos and Dynamical Systems by Alligood, Sauer, and Yorke, and I am having trouble seeing how one of the steps in a proof follows from the assumptions. I provide a statement ...
3
votes
1answer
84 views
What is a good text on bifurcation theory?
What is a a good text on bifurcation theory for mathematicians who haven't seen it before?
I'm looking to get a feel for the intuition behind the subject, major standard theorems, etc. I do not mind ...
0
votes
1answer
42 views
Is there a bifurcation node in the activation energy of chemical reactions?
I was thinking about the activation energy of chemical reactions (obviously), and I was wondering if there exists a bifurcation node somewhere in the transition state. Let me give you a link to an ...
1
vote
0answers
36 views
Half-stable fixed point on a circle
On a line graph, it's clear that a half-stable fixed point is the limit of moving the unstable fixed point towards the stable fixed point. Some solutions go to infinity depending on the initial ...
2
votes
2answers
125 views
Period doubling is chaos?
I've already read something about chaos and it's origins but I am not sure that this affirmative statement is true for all the cases. Can anyone help me? Thanks, Bruno
0
votes
0answers
69 views
The equation $2 \cosh(3.1786803659501505 z) = z$?
Let $a$ be a positive real number and $z$ a complex number.
I was wondering about the equation $2 \cosh(a z) = z$ where we solve for $z$.
Clearly if $z$ is a solution than so is its conjugate.
It ...
