Questions tagged [chaos-theory]

Chaos theory is the study of systems that are highly sensitive to slight, even imperceptible changes in initial conditions. This is popularly known as the butterfly effect. Many natural systems exhibit chaotic behavior, including weather and electron orbitals.

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Is there any theory of model in theoretical physics akin to Wheeler's ide of "Law without law"?

When trying to explain from where did all the laws come from, John Wheeler proposed the anaphorism of "Law without law". He proposed that at the "beginning" there were no laws ...
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How does object move in bottom of swimming pool? [closed]

Suppose there is an object $O$ (swimming goggles) that has fallen to the bottom of a swimming pool. I have the swimming pool circulation pump turned on. Initially, the object is at some position $P_1$....
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Planning new project on sensitivity analysis of simulated crystals [closed]

Not a while ago, I began to read about negative thermal expansion and I started reading about all the work Linus Pauling had done with ice crystals. I am meant to be doing a 7-month research project ...
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Predicting algorithms [closed]

is it possible to predict an algorithm (roulette for example) by using a number of independent bifurcation points in equal increments and studying the random pattern until it has repeated itself ...
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Are chaotic systems the same as dissipative systems in inverse time?

Lyapunov exponents define whether a system expands or contracts in phase space and can be used to determine whether a dynamical system is chaotic, conservative, or dissipative. In the volume expands ...
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Is the motion of a particle in the surface of a torus always periodic?

I am trying to see if there are ballistic trajectories in the surface of the torus that are not periodic and to what extent. Maybe it is not only quasiperiodic but chaotic. I guess there are ...
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How chaotic is the double-pendulum if the arms are not perfectly rigid?

The double pendulum is a famous example of a chaotic system. It consists of one pendulum hanging from the end of another pendulum, which in turn hangs from a fixed point. In the traditional version, ...
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Is there a relationship between quantum physics and chaos theory on a classical scale?

Im a complete physics lay person and I read somewhere that chaotic systems are subject to tiny differences in initial conditions and that the brain is a chaotic system. Does that mean our thoughts are ...
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Is there a Hamiltonian system composed by three particles which is chaotic?

The Henon-Heiles system is the smallest Hamiltonian system where chaos has been observed. Smallest because it is composed by two degrees of freedom. What is a Hamiltonian system with $n=3$ degrees of ...
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Have I spotted real-world properties of chaos theory? [closed]

I know it says no financial questions but I think this is more of a physics question... I'm an artist by profession but I like to study science as a hobby. I was researching chaos theory around the ...
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What is the precise relation between level compressibility and the spectral form factor?

In the study of disordered conductors, the level number variance is defined as $$\Sigma_2 (\langle n \rangle) \equiv \langle n^2 \rangle-\langle n \rangle^2 ~, $$ where angular brackets denote ...
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Is there a general equivalence of spectral correlations between hermitian and unitary random matrix ensembles?

It is common lore that the Gaussian Unitary Ensemble (GUE) and Circular Unitary Ensemble (CUE) have the same spectral correlations as the order $N$ of the matrix goes to infinity, see e.g. section 5.9 ...
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What are the symmetries of circular billiards that makes it integrable?

I have often heard that integrability in is equivalent to extensively many conserved quantities $A_i$, i.e. the Poisson bracket $\{H,A_i\}=0$ or in quantum mechanics $[H,A_i]=0$. What are the ...
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How can one distinguish between a random process and a chaotic process? [duplicate]

Chaos is not a random process, although it may look like one. If I am given a set of observations, is it possible to determine if the observations are generated by a random process or if they are ...
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Chaos of the Duffing oscillator: Where's the third dimension?

It's often said that all continuous chaotic systems must have at least three dimensions of phase space. The Lorenz system has three explicitly, the double pendulum has four (two angles and two angular ...
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Deterministic and stochastic chaos

I have a question about chaos, but first a foreword of what I understood. Noise refers to the random variation of values. Usually unwanted, noise causes a measurement to fluctuate over time. Chaos ...
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Eigenvalues of system with 5 or more degrees of freedom?

When finding eigenvalues for a system consisting of a single particle, its position and velocity are used when making the system of equations. So that there is an equation like $\dot{x} =\begin{...
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Analytical expression for density of random matrix level ratios

Consider a hermitian matrix $H$ with eigenvalues $E_{i-1}<E_i$. The level spacings are defined as $s_i=E_i-E_{i-1}$ and the level ratios as $r_i = s_i/s_{i-1}$. To make the support of an underlying ...
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Relative Phase distribution for two coupled van der Pol oscillators where one has a Drive?

I was solving the dynamics for a driven coupled (inertial) van der Pol oscillators, where only one oscillator is driven. I started with the complex amplitudes $\alpha$ for both of the systems which ...
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Computing correlation between two time series: confusion regarding nonlinear relationship and nonlinear data

I am trying to understand if correlation can be computed between two time series generated from two different initial conditions for chaotic dynamical systems. In general, correlation is applicable ...
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What is a uniform measure over a unit square?

Going through some reading material on two-dimensional maps, I came across the following text in reference to the Baker's map: "Consider the map: $$ x_{n+1} = \begin{cases} \lambda_a x_n & \...
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What are the implications of deterministic chaos: useful or detrimental? [closed]

I am new to the concept of chaos theory and as a layman I am struggling to understand what is the significance and implication of chaos in ecological systems such as the chaotic predator prey model. I ...
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Are chaotic systems examples of complex systems?

I am struggling to find a proper source or reference where examples of complex systems which are chaotic are given. Based on my understanding, complex systems consist of interacting components, each ...
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Poincaré maps and how they are used in dynamic systems [duplicate]

I am trying to find a solid definition for what a Poincaré map is and how they are used but the ones online are very complicated. Can someone explain with a simpler definition of what a Poincaré map ...
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Thermalization of perfect incompressible fluid

Suppose we have an perfect incompressible fluid (no viscosity) in a box. Lets assume we shook the box and let the fluid sit for a long time. Since there is no dissipation, the energy is conserved. Is ...
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Is consciousness likely to be a result of chaotic, or random processes? [closed]

Given that just about everything in the universe at a non quantum level is deterministic, what does this say about free will and consciousness? Are these likely to be a result of randomness at the ...
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Lyapunov Exponent of the Logistic map [closed]

My dynamical system professor (and the textbooks we use) all claim that the Lyapunov exponent for the Logistic map with $r=4$ ($x_{n+1} = 4x_n(1-x_n)$) is $\log(2)$. Would someone be able to sketch ...
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"Non-analytic interaction"...what does it mean?

Reading an article about Hamiltonian chaos, I found this passage: Importantly, the few Hamiltonian systems for which the KAM theorem does not apply, and for which one can prove ergodicity and the ...
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Chaos Bound in BCFT

What is the Chaos bound in boundary conformal field theory (In 2d or in higher dimension)? can one derive much restricted bound in these settings?
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When is molecular chaos dynamical chaos?

It is very common to have uncorrelated velocities in chaotic dynamical systems. Yet, we should be wary in equating the two quite different meanings of chaos. Instead of matching dynamical chaos to ...
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Uncertainty propagation in dynamical systems

I'm not a physicist, my training is in math and CS. If anything in this question is ill defined or doesn't make sense, say so in the comments and Ill try to fix it. Suppose I have a discrete dynamical ...
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Non-Analytic Equations and Chaos

Could anyone please tell me an example of an equation with no analytic solution(s) that is not a chaotic one? And what is the physical meaning of having analytic solution? For instance, the three body ...
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Generalizations of Feigenbaum universality for multidimensional maps and ones with multiple order parameters

Feigenbaum showed that for discrete 1D dynamical systems with a (smooth) unimodal evolution function, the route to chaos is universal, and depends only on the order of the map's maximum. (I'm told ...
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Can phase trajectories intersect for non-autonomous system?

There has been enough discussion about intersection of phase trajectories in autonomous system,where the system wasn't time dependent. And we came to the conclusion that, at a point in space there can'...
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Is the universe's Kolmogorov complexity growing over time?

The Kolmogorov complexity of a deterministic universe is constant. The Kolmogorov complexity of a nondeterministic universe grows over time. It grows whenever something happens that is not ...
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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 ...
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What causes water droplets to drop in periodic, but not uniform time intervals?

A little while ago I noticed water droplets forming from a slightly overflowing reserve in my sink. They dropped in a special periodic time pattern, which was not uniform. Instead two droplets would ...
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Level spacing distribution

I have started learning level spacing distribution and it says that level spacing distribution for classically regular system show poison curve. But is it valid for the integrable system as well, ...
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What prevents chaos theory from being the principle of a deterministic universe?

One could potentially suggest observations of atomic locations partly with chaos theory by suggesting that the seemingly random pattern simply results from a sufficiently small Lyapunov time that ...
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Semiclassical quantization of chaotic classical system

So far in the introduction of quantum chaos, I have read that in the early day's physicists quantized classically chaotic systems but could not find any signature of chaos in quantized systems. My ...
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Can we have chaotic motion due to the finite precision of our calculations? [duplicate]

I understand chaotic motion to mean that very small perturbations in the initial starting condition can lead to very different trajectories in phase space. For this reason, we can never predict the ...
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How do we know chaotic systems are actually chaotic and not periodic?

The usual way to calculate how chaotic a system is would be to measure the divergence rate using the Maximal Lyapunov exponent, but it requires you to wait until infinity, measure the divergence, then ...
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How to compute the connected spectral form factor for integrable models?

Given a spectrum of $N$ real eigenvalues, $\{E_m \}$ of some Hermitian operator, the connected spectral form factor is defined as follows: \begin{align} K_c(t) = \langle \sum_{m,n=1}^N e^{it (E_m-E_n)}...
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How does a discrete map (logistic map being only one such map) relate to a Poincare section?

Basically the title. I am wondering if there is a relationship between the two, and if so, what is it?
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Is there a mathematical way to determine if a force, phenomena or physical entity is in a state of chaos?

We often talk about chaos, but is chaos an objective term or a subjective term? If it's an objective term, is there a mathematical way to determine it? Is it possible there's a threshold where ...
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Probabilities for quantum random number generators

Consider a quantum random number generator (QRNG) X, which generates integers at random. (Apparently, due to quantum statistical properties, this type of generation is truly at random, see e.g. "...
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The "real butterfly effect"

This question stems from the confusion that I feel after reading this popular blog post by Sabine Hossenfelder. It is based on this paper which is paywalled, unfortunately. The claim is the following: ...
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Why is the predictability of the solar system in the Lyapunov timescale limited to 5 million years?

Is this due to a mathematical problem that is not solved? Or could this be due to our current amount of information regarding mass and other such factors in our system?
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Three body problem - Half Life

I did google this up but found nothing! I can't be the first to ask (the vague question) "What is the half life of a gravitating three-body system?" CLASSICALLY this means: Say I have three ...
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Is a satellite orbit around the Earth Lyapunov stable?

Presume there is a satellite orbiting the Earth in an orbit that follows a closed path around the planet (that is, escape orbits are not permitted here). As I understand it, there are two ...

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