Chaotic Definition and 65 Threads

Can you swap out the RNG that is the wave function collapse with a suitable deterministic chaotic process that matches the wave function (squared)? I can picture a multi leg pendulum swinging around drawing out the wave function. The point where you measure is the point the pendulum was at. Is...

Hello everyone, This is a question related to a research article involving a chaotic system that required to be solved numerically. I was trying to employ one of the spectral methods to solve the two dimensional version of the so called Rossler chaotic system...

Nauka, a Russian multipurpose science module and one of the largest ISS modules, was docked to the ISS. During the checkout procedures after docking the module suddenly fired its thrusters, rotating the ISS quite rapidly (up to 0.5 degree/s). The Zvezda module and a docked Progress resupply ship...

Here is the Chen System I am given the initial condition (t=0) that a particle lies on the xyz-plane at a point (-10,0,35). I was notified that if I plugged in a=40, b=5, and c=30, the trajectory of the particle will be chaotic. On the other hand, if I retained the values of a and c, and...

I am having a hard time understanding the discussion of chaotic sets on invariant manifolds as given in Chaos in Dynamical Systems by Edward Ott. If the invariant manifold of a particular system contains a chaotic attractor ##A##, then the transverse Lyapunov exponent ##h## will generally...

Hello everyone. I have read on the web some people that mention something about "stochastic chaos" but I am not that sure about what it really means or if that actually exists. Two months ago , I started to study some chaotic systems but in stochastic systems I am not that familiarized in...

Problem gives these for a chaotic model; V(Φ)=Voexp(-√(2/p)* Φ/Μp) Φ(t)=√(2p)*Mpln[√(Vo/24πp2) *t/Mp] There's a standard method to follow and find the a(t) by using Friedmann's and inflaton equations. I think my mistake is most likely on the math part, because in the physics aspect we always...

Greetings! Hey, can anyone help me? I need an explanation how can Lyapunov help me to check the system weather it is chaotic or not. Let say I have this equation Rossler System Eq.(1) So how can you tell that the system have chaotic behavior or not? Does it depends on parameters? or from...

Hi, I was pondering a question after seeing a video about chaotic magnetic pendulums. If you were to suspend a magnet on a pendulum above a repelling magnet, would it stop moving or would you get perpetual motion? My guess is it would stop moving but I can't think of how. Gravity would try to...

Cosmological fluctuations from equilibrium are best described in the Boltzmann brain paradox. My question may very well be better suited for statistical mechanics but it has relations with cosmology so I'll post it here. Anyway, it is often stated that BBs will perceive chaotic observations...

I have never seen a problem as such; A mass in the isocentre of a box. The springs are identical unstretched length, they are attached to the walls maximally distant from each other. The mass is suspended from springs attached to the walls of the box.What is the least number of springs to have...

Hi. I am an undergrad student taking a course on dynamical systems. Our final assignment is to find and study a dynamic system (not necesarily mechanic, but chaotic, natually). I was wondering if there is experenced people in this community that could help me find an interesting system or...

The system in which I tried to calculate the Hamiltonian matrix was a particle in a stadium (Billiard stadium). And I used the principle where we take a rectangle around the stadium in which the parts outside the stadium have a very high potential V0. We know the wave function of a rectangular...

Hello, I'm not very familiar with this problematics. So sorry for (maybe) incomprehensible terminology. I study physics and math and now I heard about chaotic behavior of many very fundamental equations describing a nature, when they evolve (when we want to know what will happen in future). I...

Does chaotic inflation involve phase transition, and if not, when does the phase transition of the breakdown of GUT symmetry occur?

Take the sequence 1,2,3,4,5,6,7,8,9,10... If you found the percent change for each interval and kept on finding the percent change of the percent change of the sequence, why does the change become more and more chaotic? Here is a quick table I made...

I work with an electromagnetic molecule trap, and I'd like to determine which orbits are chaotic. To this end, I intend to study the evolution of a perturbation on a trajectory with time. I'd like to compute something called the fast lyapunov indicator for various trajectories y(t), where I...

Hi. As far as I know, the movement of a harmonic oscillator normally is not considered to be chaotic. Why not? Since the angular frequency can never be known to absolute precision, an error in the phase builds up. I can see that this build-up is only linear in time (if we assume the angular...

Does anyone have an intuitive idea for the statistics of chaotic light? I can understand that the power fluctuations in this kind of light can give rise to a second order autocorrelation parameter g(2) higher than 1. However I can not see why the value for this parameter should be g(2)=2. Does...

Homework Statement It's problem 4:[/B] https://scontent-sea1-1.xx.fbcdn.net/hphotos-xpa1/v/t1.0-9/12004675_10206509414950788_2644752353357758096_n.jpg?oh=e6292fae7cdc34b881c7ac31a506e315&oe=56680268 Homework Equations The Wiener Khinchin theorem gives that the normalized spectral power...

So, I was playing around with a couple of voltage multiplier circuits a few months ago, and while optimizing one design, I came up with a pretty neat (not to brag) way of converting a sine wave to a square wave by using transformers in a completely different way than normally. A little while...

What am I trying to do? I'm trying to implement a simulation of a chaotic billiard system, following the algorithm in this excerpt. How am I trying it? Using numpy and matplotlib, I implemented the following code What is the problem? When calculating phi_new, the equation has two solutions...

The field equations of general relativity are non-linear. There are exact analytic solutions to the equations for special symmetrical cases, e.g. Schwarzschild's solution for a black hole. But in general, wouldn't there be other chaotic solutions as well? A chaotic system is analytically...

windows screen capture So I built this circuit(Chua's chaotic circuit) and I have to take it to the lab for plugging it to oscilloscope.I need to make sure it works, cause I won't have any time there to fix it or rebuild it.So when I i tested it with the multimeter,there was no voltage on the...

If a person gets a phd studying controls theory, shouldn't they have the skills (as a researcher) to publish electrical engineering research one year, economics the next year, and biology the next? Since someone that studies "systems" generally works in high abstractions, I don't see why the...

Homework Statement I'm working on an assignment about the chaotic behaviour of the Duffing Oscillator, using Wolfram Mathematica, which has a package that can be used to calculate Lyapunov exponents. From looking the oscillator up online, I have a set of parameters that result in...

Can anyone explain to me why after chaotic inflation with V=\frac{1}{2}m^2 \phi^2 that the inflaton behaves as; \phi=\frac{m_p}{m \sqrt{3\pi}t} \sin(mt). because this doesn't satify the slow roll conditions or the eqn of motion for the inflaton. I have read that it asymptotically approaches...

I am working with a Daedalon chaotic pendulum for an experimental physics class. The pendulum is rather old and seems to have a strange problem. The pendulum can be driven by a DC current, and as voltage is increased, the pendulum begins to rotate. The pendulum is supposed to rotate smoothly and...

I am little confused about the right place to ask this question but anyway here it goes: How can one convince oneself that (if at all it is true) chaotic attractors always are fractals? Thanks in advance. P.S.: Little bit of googling suggested that there are examples of non-strange chaotic...

so i have been studying chaotic system in class, and i just want to know if we change the initial conditions of a chaotic system can it become non-chaotic? I think yes because, chaotic system is sensitive to initial condition hence it would have an effect on the chaotic behavior. I'm I...

Hi, I am not currently studying, have never studied Astrophysics, so will no doubt come across as rather inadequate in trying to clarify, what my question actually is. Please forgive me for not using appropriate terminology, and, if this forum is not for the curious laymen in the general...

Hi first time poster. I have a question which has been intriguing me for some time. Are most chaotic systems also chaotic if played backwards in time? For example if we played a video of a double pendulum, will it exhibit the similar chaotic behaviour if played to someone in reverse? I guess the...

Hi, I want to do a similar statistics analysis as in the next paper: http://www.phy.bris.ac.uk/people/Berry_mv/the_papers/Berry340.pdf But the boundary conditions are on a two dimensioanl torus, so a solution will be of the form u(R)=\sum_{j=1}^{\infty} \sum_{m,n=0}^{\infty} (A_{mn}...

This text patch is taken from wikipedia article http://en.wikipedia.org/wiki/Julia_set "For f(z) = z2 the Julia set is the unit circle and on this the iteration is given by doubling of angles (an operation that is chaotic on the non-rational points). There are two Fatou domains: the interior...

Why a chaotic system always bounded? What factor control the boundedness?

Homework Statement If there's a satellite(not man-made although I wonder it would matter) is chaotically orbiting around two planets, will it ever cross the same orbital path twice or not? Homework Equations The Attempt at a Solution I think if the system is chaotic, it will not...

I'm not sure if this is the forum for this question. Anyway, I was wondering if the universe has orderly, chaotic, or has a measure of both? I see aspects of order when it comes to the nuclear force that tends to have order to it. However, I can't help but find the inner workings of a...

1. Homework Statement I am studying Henon Attractors. The Henon map is recursively defined as follows: x_{t+1} = a - x^2_{t} + by_{t} y_{t+1} = x_{t} I am supposed to find the fixed point (may be unstable) that is contained with the chaotic behavior The Attempt at a Solution It is clear...

How do you feel about it? I just want to know what some intellectuals think about it. Personally, I think we live in more of a chaotic universe where chance and probability rule supreme, as told from Quantum Mechanics.

Any thoughts on the article in Science Daily this week regarding the Universe being chaotic immediately following the Big Bang?

Consider a dynamic system with a periodic trajectory. Given an arbitrary duration T of time, does there exist a chaotic trajectory of a similar system which approximates the closed orbit for the duration T with a given accuracy? Chaotic orbits which I've seen so far...

I'm currently reading a book by Michio Kaku, a theoretical physicist, and mentions this theory in his book, he dosent discuss much about and i am wondering if anyone has any comments on it. Thank You

I don't know much about biology, my background is in maths and physics. Hopefully someone else here knows it better than me. Anyway, I was wondering if evolution would go the same way if it were repeated again with the same (or very nearly the same) initial conditions. I'm not sure how much...

Can we consider a stochastic process being chaotic? consider evolution of only two particular systems with closed initial states (not ensemble or statistical properties of the system)

Hi Guys, Okay I have a question i was wondering if anyone can enlighten me on this discrepancy. I asked Gavin Schmidt on RC whether he thought the climate was a chaotic system. He said he did not know (seriously). What i fail to understand is how can anyone be confident about the...

Are the two words interchangeable?

I hope someone can help me understand some inflation principles. In Alan Guth's popular book: The Inflationary Universe, he presents a schematic of a false vacuum universe decaying into pocket universes. The false vacuum expands exponentially as the pocket universes are continuously...

When using the Friedmann equation (flat space, no cosmological constant): H = sqrt (8 pi G / 3 ) * rho, if we use rho in mass/volume, H is in (time)^-1 like it should. Now for some inflation models, we use: H = sqrt (8 pi G / 3 ) * V(Phi). It seems that V(Phi) should also be able to be...

Chaotic systems are defined in terms if extreme dependence on initial conditions. Very small changes in initial conditions result in large scale variations "downstream". The implication is that if we know the initial conditions exactly, we can know the system's behavior exactly as it evolves...

Is chaotic inflation eternal into the past forever, as well as into the future forever. In the theory was there a beginning to it, or has it always been?