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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What are the differences between logistic map, poincaré map, attractor, phase portrait, bifurcation diagram? [on hold]

What are the differences between Logistic map, Poincaré map, Attractor, Phase portrait, Bifurcation diagram Currently I became interested in chaos theory and non-linear dynamics. While ...
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Is there any book about chaos theory and nonlinear dynamics? [duplicate]

I'm interested in chaos theory and nonlinear dynamics. I learned some knowledge about phase space, attractors, bifurcation diagram, etc from Wikipedia. But I want to study more comprehensive about ...
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Why is my Lyapunov exponent similar for single and double pendulum?

This is my first question here on stackexchange. I hope that I can be understood. If not, tell me and I will reformulate and fill in with details. I have simulated a single pendulum and a double ...
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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 ...
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On the application of chaos in signal processing [migrated]

Paper: A novel channel equalizer for chaotic digital communication system (DOI, RS link). I am having problem in understanding their claim which is that a nonlinear system, considered here to be a ...
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Can I use the Chi squared test to see if my data fit to the Wigner-Dyson distribution indicating chaotic behaviour? [migrated]

I recently read the paper about Quantum Chaos in Feshbach resonance spectra of ultracold Erbium [1]. The authors analyze their data statistically using the random matrix theory framework for ...
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Help explore a self-feedback camera-monitor chaotic system

We are trying to emulate the chaotic system Jim Al-Khalili demonstrate (3 min video). In our chaos lab, we are trying to research the chaotic system shown in the video. We are using just a webcam and ...
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What creates the chaotic motion on a double pendulum?

As we know, The double pendulum has a chaotic motion. But, why is this? I mean, the mass of the two pendulums are the same and they have the same length. But, what makes its motion random? I'm just ...
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Can binary sequences generated from ergodic maps be chaotic?

Chaotic Sequences of IID Binary Random variables with their applications to Communications and related papers by the same author, Tohru Kohda, talk about the statistical properties of binary symbolic ...
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Theory of chaotic systems : Bijective mapping

Considering a one-dimensional chaotic map $T$. The domain of the map (the closed interval $[0,\,1]=I_1 \cup I_1$) is partitioned into two regions (i.e. $I_0\cap I_1=\emptyset$): $[0,\,A] = I_0$ and ...
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Why is the computer useful if a chaotic system is sensitive to numeric error?

In every textbook on chaos, there are a lot of numerical simulations. A typical example is the Poincare section. But why is numerical simulation still meaningful if the system is very sensitive to ...
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Origin of chaos in Chua's circuit

I am doing a project on Chua's circuit, but I can't seem to find anything that explains where the chaotic nature of the system comes from. Does anyone know of articles that explain it well on an ...
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Ratio between power of chaotic and regular airflow

Turbulent field is created as a result of an impact of an airjet on an edge (the flow velocity is high enough). The field of velocities have a regular and a chaotic component. What I need is to ...
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Current scope of Chaos theory and non-linear dynamics? [closed]

I am a physics undergrad interested in stuff like dynamical systems, chaos theory etc. Is there ongoing research in these fields? I am talking about pure research and not applications to things like ...
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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 ...
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Does big bang have really any justification while we are living within a huge chaos?

All the physicists already know that the n-body problem reveals chaos, so that the planets around the sun should undergo deterministic chaos with a Lyapunov exponent of the order of, say, ...
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Hysteresis in the Lorenz Equations

I was going through Strogatz's wonderful book on nonlinear dynamics and while reading through one problem he posed at the end of the chapter, I did not really understand what was going on. So I hope ...
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51 views

Can quantum fluctuations affect the double pendulum?

The double pendulum is a simple example of a chaotic system which is extremely sensitive to tiny perturbations in its initial conditions. If we set off two identical double pendulum systems from ...
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Quantum chaos vs classical chaos

There is this popular conjecture from Bohigas, which says: When the analogeous classical system of a quantum system shows chaotic behaviour then the spacing distribution of the quantum system ...
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Nearest Neighbour Spacing Distribution - Quantum chaos

it's always mentioned that the NNS of a "regular" quantum system follows a Poisson distribution. But when I have a look at this picture: for example when I look at F=500V/cm, where I'm in the ...
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Question on the stability of the solar system

One of the pertinent questions about many body systems that causes me much wonder is why the solar system is so stable for billions of years. I came across the idea of "resonance" and albeit an useful ...
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Determining the geometry of the phase space of a system [closed]

How do we check the geometry of the phase space ? I mean in classical mechanics we use position and conjugate momenta as a space of all possible states of the particle. How do we know that this phase ...
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What is the relation between Rössler attractor and thin accretion discs (like in the movie Interstellar)?

Is there any relationship between the Rössler attractor and thin accretion disks, like the accretion disk(s) in the movie Interstellar?
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Quantum Chaos - Level spacing distribution in integrable quantum systems

For an undergraduate essay, I am studying the development of quantum chaos in a 1D spin 1/2 chain (my main source paper can be found here: ...
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What are resonant tori?

What is the definition of a resonant/invariant torus (in the phase space of a Hamiltonian system)? Are there non-resonant tori?
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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 ...
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Mapping between numbers and symbolic representations

I am not a physicist but applying symbolic dynamics for information coding in signal processing. Is there any mapping between symbols and numbers?
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What is discrete phase space?

I've been reading a little about the usual, continuous Wigner functions and phase space quasi-distributions in general, and I believe I understand the idea behind them. The Wigner function arises when ...
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Importance of periodic orbits

In the study of dynamical systems, one often talks about solutions that repeat themselves after a certain time, hence their name of "periodic orbits". Then one moves to the distinction of "stable" ...
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Non-integrability of the 2D double pendulum

Context: For a system with $n$ degrees of freedom (DOF), one has to deal with $2n$ independent coordinates ($2n$ dimensional phase space), of position $q$ and $\dot{q}$ in Lagrangian formulation, ...
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How far ahead can we predict solar and lunar eclipses?

The solar system is non-integrable and has chaos. The sun-earth-moon three-body system might be chaotic. So, how far into the future can we predict solar eclipses and/or lunar eclipses? How about ...
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Is it really impossible to calculate in advance the result of throwing dice?

Is it really impossible to calculate in advance the result of throwing dice? After all, the physics of dice throwing is in the world of classical mechanics, rather than quantum mechanics.
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Does the logistic map have an attractor for a particular value of the parameter?

Background: Currently I am studying a course on non-linear dynamics. We have been studying about attractors only intuitively, so I do not have a definition for an attractor. Let me give you a couple ...
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The natural metric of a phase space and the Lyapunov exponent

For me, it seems that there is no apparent metric on a phase space of a dynamical system. Of course one can naively define an Euclidean metric on it, but it seems that this metric has not much to do ...
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What is the temperature evolution of the conductance of a quantum chaotic system?

I read this really nice article by Abanin and Levitov: http://arxiv.org/pdf/0704.3608.pdf They argued that the mixing of the quantum edge channel at the vicinity of a PN junction is described by the ...
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Is quantum indeterministic? [duplicate]

The question might look clear from a viewpoint of a non-physics guy but let me be more specific. Can we say quantum leaps or waves or maybe the universe itself are completely indeterministic or do ...
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Meaning of Smooth Dynamical System?

What does smooth dynamical system mean? It is the title of a paper I am supposed to read in non linear systems.
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Physics-oriented books on fractals

I'm looking for some good books on fractals, with a spin to applications in physics. Specifically, applications of fractal geometry to differential equations and dynamical systems, but with emphasis ...
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Making new sense of the three-body problem in the light of Maryam Mirzakhani math contributions

I am unfamiliar with moduli spaces and ergodic theory which appear to be essential in Maryam Mirzakhani's math contributions which won her the Fields Medal. However, I am well conversant in essential ...
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Diffusion in the standard map

Consider the standard map (also known as Chirikov map): $$ p_{n+1} = p_n + K \sin(\theta_n) \\ \theta_{n+1} = \theta_n + p_{n+1} $$ I know that the diffusion coefficient according to the ...
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What do matrices in the Gaussian orthogonal ensemble look like?

I've been reading a fair amount about quantum chaos, and random matrix theory comes up a lot. I get that they're looking at the distribution of eigenvalues from an ensemble of random matrices, but I ...
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Is chaos theory essential in practical applications yet?

Do you know cases where chaos theory is actually applied to successfully predict essential results? Maybe some live identification of chaotic regimes, which causes new treatment of situations. I'd ...
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Chaos theory and determinism

My professor in class went a little over chaos theory, and basically said that Newtonian determinism no longer applies, since as time goes to infinity, no matter how close together two initial points ...
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Interpretation of Poincare Map

I have been trying to interpret a Poincare Map. The Hamiltonian for the system is $$H=\frac{1}{4m}\left(p_r^2+p_z^2\right)+m\omega_\perp^2 r^2 +m\omega_z^2 z ^2+ ...
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Does a simple double pendulum have transients?

Suppose, we have the most simple double pendulum: Both masses are equal. Both limbs are equal. No friction. No driver. Arbitrary initial conditions (no restriction to low energies) Does this ...
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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 ...
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How classical chaos can be described quantum mechanically?

How can we describe the chaotic properties of classical systems using quantum mechanics when the Schrodinger equation that describes quantum dynamics is linear? How can we use quantum mechanics that ...
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Dynamical localisation in delta-kicked rotor

The quantum delta-kicked rotor is a common tool for studying quantum chaos. The energy of the rotor increases ballistically when kicking at the Talbot time (resonance) and jumps between zero and some ...
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Chaos theory deterministic or non-deterministic?

While i was studying about chaos theory, i stumbled upon this, When a ball confined in a square, and at the center is located a circle, is to bounce elastically, the path of the object deviates ...
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Logistic map and attractors

Does the logistic map have a strange attractor for some "chaotic" values of the parameter?