Questions tagged [bifurcation]

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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 ...
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40 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 ...
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41 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 ...
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1answer
48 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 ...
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26 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 ...
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1answer
43 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 ...
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1answer
65 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) ...
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2answers
88 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 ...
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2answers
516 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 $\gamma$ ...
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1answer
119 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? ...
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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 ...
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1answer
462 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?
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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 ...
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98 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://...
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2answers
144 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 ...
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171 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 ...