Questions tagged [bifurcation]
The bifurcation tag has no usage guidance.
18
questions
1
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0answers
29 views
Solutions to Chen System/Attractors
I have a problem involving the new chaotic system dubbed as the Chen System. This involves a system of coupled nonlinear ordinary differential equations. My problem is to determine for which ...
0
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0answers
21 views
Malkus Lorenz water wheel
I have read a paper by Leslie E. Matson named "The Malkus-Lorenz water wheel revisited" published in the American Journal of Physics in 2007. There the author has discussed about the ...
0
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0answers
20 views
How can I use bifurcation analysis of the Lorenz system in calculating the fractal dimension by the Spectral decay coefficient method?
Discrete Fourier transform represents data by a superposition of sines and cosines that have various amplitudes and frequencies. With time series of length N, the range of frequencies that can be ...
2
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0answers
42 views
Bifurcation of Van Der Waal equation for real gases
Van Der Waal's equation leads to a cubic equation in v of the form
$$Pv^3-(bP+RT)v^2+av-ab=0$$
This equation has 3 roots for $T<T_C$ and one root for $T>T_C$
I understand why region ABCDE is ...
1
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0answers
42 views
Bifurcations in Statistical Physics
I am currently a grad level student in physics with much interest in statistical and soft-matter physics (equilibrium and out of equilibrium); I am currently taking a course in numerical methods for ...
0
votes
1answer
50 views
Path between fixed points in logistic map
I have a question about period doubling and fixed points in the logistic map. Let's say I have a basic logistic map, $$f(x) = 4\lambda x(1-x).$$ Let me then compare 1,2 and 4 iterations of this map on ...
1
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0answers
27 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
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1answer
44 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
76 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
91 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 ...
2
votes
2answers
589 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
127 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
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1answer
40 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
516 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
1k 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
104 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
145 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
172 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 ...
