# Questions tagged [bifurcation]

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### 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 ...
113 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? ...
394 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?
707 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 ...
55 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) ...
82 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 ...
23 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 ...
341 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 $\gamma$ ...
85 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://...
40 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 ...
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 ...