Questions tagged [bifurcation]
26 questions
3
votes
2 answers
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 used to describe stable points for periodic motion. I have also read about how bifurcation diagrams describe changes in positions of visible stable points of a system with respect to…
user191954
3
votes
1 answer
Are bifurcations in dynamical systems related to phase transitions?
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?
A.Biswas
- 31
3
votes
0 answers
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 natural frequency of the system.
The…
turnip
- 3,768
2
votes
1 answer
Phase space portrait for dynamical system with Bifurcations
I have this dynamical system
$$x'=y, y'=-x^3-y+mx$$
and I want to draw the phace space diagram for $m=-1/8, m=1/4,$ the bifurcation points. 1st of all I cant find what kind of bifruction I have( I go from stable focus to stable node and sadle), does…
Kostas_vaf
- 21
- 1
2
votes
1 answer
What type of bifurcation is this?
Consider the dynamical system
$$
dx/dt = -\cos(r)\sin(x)
$$
Clearly $x=0$ and $x=\pi$ are two fixed points of this system.
The stability of these two fixed points change as r is varied. Starting from $r=0$, the zero fixed point is initially stable…
2
votes
0 answers
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 $TT_C$
I understand why region ABCDE is physically unrealized (for path ABC pressure goes down…
Rumman
- 41
2
votes
3 answers
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 $\gamma$ in the range $1.060 \leq \gamma \leq 1.087$:
I…
Damian Anslik
- 21
- 4
2
votes
1 answer
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?
And there are many other natural systems that…
kryomaxim
- 3,558
2
votes
1 answer
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 eigenfrequency refers to the static stability of mechanical…
Bzhenko
- 21
1
vote
1 answer
Are one-dimensional bifurcations dissipative or conservative?
I have elementary questions about one dimensional bifurcations.
It should be remarked that I have also searched and read previous posts of Physics stack exchange. However, these did not help me with the questions to be presented here. Owing to the…
VH84
- 13
- 2
1
vote
0 answers
Inhomogeneous Brusselator model
I am studying a Brusselator model which includes inhomogeneous terms such as $\nabla ^2 x$ and $\nabla^2 y$ in the following way
\begin{aligned}
&\partial_{\tau} x=a-(b+1) x+x^{2} y+d_{X} \nabla^{2} x, \\
&\partial_{\tau} y=b x-x^{2} y+d_{Y}…
Pablo
- 151
1
vote
0 answers
Terminology for scenario when energy of system $E(\theta_1,\ldots,\theta_k)$ with $k$ real parameters, is minimum whenever $\theta_1=c$ (fixed value)
Disclaimer. I'm not a physicist.
Consider a physical system whose "energy" $E$ is a function of $k$ real parameters $\theta = (\theta_1,\ldots,\theta_k) \in \mathbb R^k$. Let $E_{\min}$ be the minimum possible energy for the system (e.g zero). Let…
dohmatob
- 193
1
vote
1 answer
Linear stability analysis of a 2-cycle
In a discrete $N$-dimensional Hamiltonian map $\mathbf{X}^{(n+1)}=f(\mathbf{X}^{(n)})$, we often find a 2-cycle which shows oscillation between two points in phase space. In such a Hamiltonian map we analyze the stability of a fixed point from the…
user101134
- 741
- 14
- 26
1
vote
0 answers
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 parameters a, b, and c would yield a periodic and chaotic…
1
vote
0 answers
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 bifurcations theory, and the course does not…
