# 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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### What are some chaotic long lasting initial conditions for the three-body problem?

I have been trying to find some good long lasting chaotic trajectories for the three-body problem, but it seems to be very hard to find. All I find on the internet is a lot of periodic solutions for ...
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### How to Interpret Solutions to Simple Chaotic Systems

Note: I'm a non-physicist so please take any misunderstandings/poor notation on my end with patience. I remember watching a pop-physics video around 5 years ago which discussed the solution space of ...
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### Area of Phase Space and Dependence on Energy

The phase curve for a system is made for some configuration, for example - The Harmonic Oscillator. Now as we increase the energy, the phase curve enlarges i.e. area enclosed by the curve increases. ...
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### A rule for when phase-space orbits may cross

Note: in this question when I talk about "phase space," I will be refering to velocity vs. position space, which can also be correctly referred to as "state space." Many sources (...
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### Graph Interpretation of Fold of Cyclic Bifurcation

I was studying about local bifurcations of cycles, and the basic type of it was the cyclic fold. According to the textbook, cyclic fold bifucation was the meaning of one of those that is, for two ...
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### Physical reasons for why systems are chaotic?

Are there any reasons why a system would exhibit chaotic behavior? Or is this something only found through numerical modelling or experimental testing? For example, the simple forced, damped pendulum ...
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### What are the conditions for RG flows to have strange attractors?

this question served as a great reference for RG flows that can end up with more complicated dynamics than fixed points, such as limit cycles. As far back as K.G. Wilson's 1971 original RG paper, ...
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### What is a "classically chaotic quantum system"?

In the context of quantum mirages one can find increased probability density around paths of unstable classical periodic orbits, called quantum scarring. In this wikipedia article they use the term &...
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### Terminology for scenario when energy of system $E(\theta_1,\ldots,\theta_k)$ with $k$ real parameters, is minimum whenever $\theta_1=c$ (fixed value)

Disclaimer. I'm not a physicist. Consider a physical system whose "energy" $E$ is a function of $k$ real parameters $\theta = (\theta_1,\ldots,\theta_k) \in \mathbb R^k$. Let $E_{\min}$ be ...
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### The Electron at the End of the Universe

In A Passion for Science, Michael Berry's essay "The Electron at the End of the Universe" poses two scenarios. Assume that a box of gas particles obeys Newtonian mechanics and that we ...
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### Why is this argument about free-will flawed/wrong? [closed]

I would really appreciate some thoughts on my argument/thought experiment. I can’t think of a logical defense of the existence of free will in the context of human action at the scale of the ...
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### Time taken for a system to return to it's original state

Consider the following system: There are N particles (point-like particles) of $1$ Kg each in a Sphere of radius $R$ centered at origin in three dimensions. Randomly assign these N particles their ...
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### Linearization of 1D maps about a fixed unstable point [closed]

Recently, I was going through the paper Controlling Chemical Chaos in a three variable autocatalator system, by Peng et al. Here are the references Although I have been introduced to 1D maps and the ...
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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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### 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 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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### 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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### 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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