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5
votes
1answer
69 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
225 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
52 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 energy ...
0
votes
1answer
43 views

Why trajectories approach to origin tangent to the slower direction?

I am reading non-linear dynamics from Strogartz. Suppose, I have two solutions of a non linear system: $x(t) = x_0e^{at}$ and $y(t) = y_0e^{-t}$, where $a\in \mathbb{R}$. Now it is clear that,for ...
0
votes
1answer
63 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
49 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
58 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
77 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
56 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
43 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
22 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
61 views

Logistic map and attractors

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

Heat Retention of Wine

This may seem odd and lengthy but I am going to attempt to consolidate my thoughts as much as possible. I'm sorry in advance for the length of my post and if this is confusing. I am currently ...
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 ...
-1
votes
0answers
41 views

How to do linear stability analysis on this system of PDEs?

I was reading this paper. The model as in the paper is given below. Is it possible to do a linear stability analysis on this system? If so can someone help me?