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5
votes
1answer
74 views

Pink noise in low-dimensional systems

Pink noise (1/f) is often cited as a signature of complex or critical systems. Is it possible for a low-dimensional time-independent first-order system to generate pink noise? Intuitively it seems ...
1
vote
1answer
257 views

Does Lyapunov exponent equate to exponential inflation?

Physics can be modeled by dynamical systems $f^t(x)$ as well as by PDEs. The most common dynamical system has hyperbolic fixed point and can be an attractor or a repellor. The dynamics at repellors ...
0
votes
1answer
161 views

Is the double pendulum an example of a strange attractor?

Imagine a pendulum to which is attached another one (not necessarily the same length). Does this pendulum, when you let it go (which can be done in many ways but let's keep the total potential ...
0
votes
1answer
86 views

Time it takes for a mass in a linked pendulum to flip?

I have created Mathematica code that simulates a double pendulum. So I've numerically solved for $\theta_{1}(t)$ and $\theta_{2}(t)$. I have also found the momentum from the Lagrangian as well. My ...
4
votes
0answers
53 views

Solutions of nonlinear systems invariant wrt. perturbations (looking for applications)

I want to ask if the following purely mathematical problem (that I'm working on) might have some applications to physics. The problem in a nutshell: describe properties of solution sets of real ...
3
votes
0answers
32 views

What is a “stochastic web”?

In this lecture-video (at about 37:17) on Hamiltonian dynamics, the instructor mentions that for an (Arnold-Liouville) integrable finite-dimensional Hamiltonian system one has the following: Phase-...
3
votes
0answers
63 views

Reference for the Landau-Lifshitz system

I'm interested in understanding the dynamics of the discrete Landau-Lifshitz system. It's solutions to equations like $$\frac{\partial X_n}{\partial t} = X_n\times (X_{n-1}+X_{n+1})$$ where the $X_n$ ...
3
votes
0answers
78 views

Kolgomorov entropy issues

I am long been confused by these entropy terms. Would be obliged if an explanation is provided in less technical jargon What are the differences between Shannon's entropy, topological entropy and ...
2
votes
0answers
57 views

Why can any pair of master coordinates be used to calculate a nonlinear mode of a nonlinear dynamical system?

This is a question I have been asking myself for some time since the following technique is often used in the nonlinear dynamics community, but never managed to get an answer why it could be applied. ...
2
votes
0answers
47 views

What does unfolding of attractor mean?

What does unfolding of attractor mean? Effect of time scales on the unfolding of neural attractors paper talks about Takens embedding theorum. It says that the embedding dimension should be large ...
1
vote
0answers
61 views

Which condition is stronger - ergodicity or mixing?

Reading a statistical physics book, I've encountered the following assertion (without further explanations): [..] the presence of dynamical instability makes the trajectory of a system much more ...
1
vote
0answers
25 views

Change of variables to apply Melnikov method

Supposing there is a system of non-autonomous non-linear differential equations with small damping and small forcing. The unperturbed system (zero damping and forcing) is Hamiltonian but neither has a ...
1
vote
0answers
63 views

Logistic map and attractors

Does the logistic map have a strange attractor for some "chaotic" values of the parameter?
0
votes
0answers
14 views

Stability of a complex valued system using Jacobian

I want to find the conditions for stability of a system by constructing the Jacobian matrix and finding what values of my parameters will give me negative eigenvalues. My system is of the form $ \dot{...
0
votes
0answers
33 views

How is wave equation equivalent to the Turing reaction-diffusion equation with 3 species?

I was reading the paper, "Critical waves and the length problem of biology" by Robert B. Laughlin. He mentions a point like this in it : "This wave equation is equivalent to Turing Reaction-diffusion ...
0
votes
0answers
33 views

Is there a thermodynamic law or theorem that expresses how systems “break” or “change” when enough energy is added?

I have a simple question about thermodynamic laws, and I am hoping you can help me. Let's say that I have a sphere container with some pressurized gas in it. I can slowly increase the pressure over ...