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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Why is the Hénon–Heiles system chaotic?
I am studying chaotic systems and classical mechanics and I am looking at the example of the Hénon–Heiles system.
As I understand by the Liouville–Arnold theorem, if a system of $n$-DOF has $n$ ...
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Fragile complex systems
Are there known complex systems that exhibit fragility in the sense that small perturbations — either in the local interaction rules between particles (or agents), or in the surrounding environment — ...
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Is there any general principle for why small deviations in models give only small errors in predictions?
I have a question regarding the pragmatic heuristic that goes something along the lines of
"Small deviations from reality in a model yield small errors in the predictions of the model"
Is ...
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From phase portrait to equation
Given a certain phase portrait/phase space, what is the right approach in order to find an equation $\dot{x}=f(x)$ (or a set of equations $\dot{x_n}$) with a flow consistent with that portrait?
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Is the weather intrinsically chaotic?
As far as I know, chaos theory emerged as an explanation to the sensitive dependency of weather on its initial conditions. Meaning that every slight inaccuracy during the measurement phase of weather ...
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Does Heisenberg uncertainty principle and chaos theory create indeterminism? [duplicate]
I’ve been struggling to understand this and hoping for an answer from someone enlightened.
Heisenberg Uncertainty Principle states there is a trade off between how much we can know about position and ...
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Integrability breaking due to bulk impurity
I was going through the paper on the effect of placing a bulk or edge impurity in the XXZ-Heisenberg model : here. Even though I can reproduce all the calculations and verify one of the main results i....
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If the clapper of a bell is another smaller bell would this be chaotic in the same way a double pendulum is?
A double pendulum is an example of a chaotic system.
Is one bell inside another the same mathematically speaking? Would we hear chaos?
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Well-posedness of initial value problem in chaotic systems?
Quoting Wald from his seminal textbook on general relativity (Chapter 10):
First, in an appropriate sense, "small changes" in initial data should produce only correspondingly "small ...
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Dynamical systems and biophysics
I would like to find a good book / lecture notes available online that applies the theory of dynamical systems and ergodic systems to the systems of biophysics, more specifically on the case of large ...
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Singular solutions in Newtonian gravity for two particles
In Earman's Primer to Determinism, he writes:
For Newtonian gravitation, the equation of motion is
$$\mathrm{(III.3) \quad}m_k\ddot{r}_k = \sum_{j, j \neq k} Gm_jm_k (r_j - r_k)/r^3_{jk} \quad (r_{jk}...
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Poincaré Sections and Return
I'm a matematician working with rigurous treatmenent of chaos. As we all know, Poincaré indicated that we should study annular/toroidal diffeomorphisms in order to understand the dynamics of complex ...
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Why do traffic jams happen even on a highway?
I was surprised to find myself in a traffic jam on a highway (it's a densely populated city). If we think of vehicles on a highway as particles flowing in a pipe, when the inflow exceeds outflow the ...
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How can a superdeterministic universe deal with (classical) chaos? [closed]
I'm aware that "superdeterminism" is sometimes misinterpreted, so I just want to provide a bit of context about how I understand the term:
When I was first learning about how a "hidden ...
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Experiments on double pendulums: Does it take the same time to stop each time I dropped them from the extended horizontal position? Why?
Experiments on double pendulums: Does it take the same time to stop each time I dropped them from the extended horizontal position? Why?
Consider you dropped a double pendulum extended from the ...
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