Questions tagged [bifurcation]
The bifurcation tag has no usage guidance.
12
questions
1
vote
0answers
21 views
Superfluid Vortex Lines Bifurcation and Winding Numbers
Vortex lines in superfluids are characterized by their quantised circulation: $k = \frac{h}{m}\times n$, where $n$ is the winding number in the sense of a topological winding number. Now, most vortex ...
0
votes
1answer
39 views
In what sense do bifurcations concern change in quality?
I've heard such vague statements several times and also read:
Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family.
(From ...
1
vote
1answer
50 views
Poincaré Map (Quasi-periodicity; Stability)
In a Poincaré map, when quasi-periodicity is exhibited by the dynamical system, what does it mean in terms of stability for the dynamical system?. Why is it so that as Maximum Lyapunov exponent (MLE) ...
1
vote
2answers
78 views
Do meaningful bifurcation diagrams exist for systems described by vector fields on circles?
I've been reading about the vector field on a circle, and how it's been used to describe stable points for periodic motion. I have also read about how bifurcation diagrams describe changes in ...
1
vote
1answer
311 views
Issue with Bifurcation Plot for Driven Pendulum
I'm trying to create a bifurcation plot for a driven damped pendulum. In particular, I'm trying to recreate the plot found in Taylor's 'Classical Mechanics' (page 484) for a driving strength $\gamma$ ...
2
votes
1answer
112 views
Why some dynamic systems can undergo sudden changes?
Everybody has observed that the weather may change from beautiful sunshine to extremely bad weather (heavy rain, stormy winds, ...) within less than half hour. What is the fundamental reason for this?
...
0
votes
1answer
39 views
What causes the emergence of patterns in a fluid (the “ in between” flows are chaotic) in rotating Couette cells?
In this video, around 26 minutes and 30 seconds, you can see that a fluid (whose velocity is made visible) in a Couette cell shows nice patterns at certain rotation velocities, while between these ...
2
votes
1answer
366 views
Are bifurcations in dynamical systems related to phase transitions? [closed]
Bifurcation is a qualitative measure for a dynamical system changing the system parameter. Does the statistical behavior in the system shows phase transition-like characteristics?
2
votes
1answer
617 views
What is linear / eigenvalue buckling analysis?
I need some simple and clear explanation of what is called linear buckling analysis and why it is also called eigenvalue buckling analysis?
In other words how natural vibration frequency or ...
1
vote
0answers
83 views
Non-Linear Behavior of Iterated Functional Maps
The universal behavior of certain iterated nonlinear function maps (ie period doubling bifurcation route to chaos): $$x_{i+1}=f(x_i)$$ have been known since Feigenbaum: (see http://...
0
votes
2answers
139 views
Solutions of symmetric equations are not invariant - is symmetry spontaneously broken?
I have a system of equations:
\begin{cases}
f\left(x_{1}\right)+f\left(x_{2}\right)+P=0\\
\\
g\left(x_{1}\right)+g\left(x_{2}\right)=0
\end{cases}
where $f$ and $g$ are some functions, $P$ is a ...
3
votes
0answers
169 views
What can I expect to see in a oscillator exhibiting bifurcation?
I have a program which aims to simulate a Josephson Bifurcation Amplifier. I am currently trying to obtain a plot of the probability of bifurcation as a function of the ratio between the driving and ...
