Sentences with phrase «of chaotic systems»

The trajectory of chaotic systems, being stuck on the attractor, can not exhibit a trend.

In this formulation the collective behaviour of the indices reflects the behaviour of the system as a whole and enables the search for behaviour expected of chaotic systems.

At the time we were not aware of chaotic systems.

I realize that much of this is completely unpredictable, but that is the nature of chaotic systems, is it not?

The future evolution of some chaotic systems seem to be uncomputable with anything less complex than a model which is essentially a totally identical parallel universe.

You can easily find such cycles in a variety of chaotic systems, like say the stock market.

However, there are kinds of chaotic systems which operate around «attractors» so that they repeat their configurations in quasi-periodic fashion.

All of these chaotic systems you are desribing do not change the internal energy of the system and will only increase entropy.

Of course there are no mysterious «stochastic» perturbations which make go away the fundamental features of behaviour of chaotic systems — Navier Stokes is deterministic and chaotic all the way down to the quantum scales.

I don't particuarly understand your point — that they use «slowing down» and «noisy bifurcation» rather than some unspecified other property of chaotic systems?

The basic science, in terms of the feedbacks, is unproven because there is no repeatable empirical evidence, and because it relies on computer modelling of chaotic systems, which can not be done in a deterministic way.

In simple principles at the heart of chaotic systems there are regime changes that are completely deterministic but seemingly random shifts in means and variance.

Weather, and its longer - term average and trend, climate, were the original examples of chaotic systems.

Due to the sensitivity of chaotic systems to initial state, by careful adjustment of the initial parameters you can come up with just about any answer you want to support just about any policy you want to promote.

I am no chaos theory practitioner but as I understand it — models of chaotic systems are intended only to show the spatial limits and the attractors within etc..

So, the argument that removal of the sun and observing a down temperature trend somehow makes the current statistical research approaches a worthy goal is to completely miss the point of chaotic systems.

Theoretical understanding of chaotic systems with continuous spatial variables is certainly lacking.

Because it isn't given and anyone with even a passing understanding of chaotic systems knows that such a valiant claim is completely baseless unless backed up by thorough treatment of the system as complex as it is.

I would like to go back to academia and build models of chaotic systems but I have a wife and family and a mortgage along with a high tax load and overbearing regulations.

The old 60 odd year climate cycle plus a knowledge of the nature of chaotic systems seem to adequately explain both phenonema in a much more straightforward manner.

The fact that you think that one needs to input some kind of special «chaos code» into the models just show that you lack a basic understanding of chaotic systems.

Based on my limited knowledge of chaotic systems, I wish to ask the following: isn't it possible (perhaps equally possible) that severe weather could become less - widespread in a warmer world?

The unpredictable character of chaotic systems arises from their sensitivity to any change in the conditions that control their development.

Moreover, what happens to an individual car is highly dependent on the weight of its passengers and where they sit — a characteristic of chaotic systems, in which small changes in the starting conditions produce wildly different results.

For example, the idea that the brain is a complex non-linear dynamic system is mentioned only fleetingly - leaving me with the feeling that we had missed an opportunity for a useful discussion (such as perhaps making a connection with the ideas advocated by Polkinghorne regarding the possibility of chaotic systems «amplifying» quantum level uncertainties up to the macro-level).

Because the ride has all the characteristics of a chaotic system, no two trips are likely to provide the same thrills and chills, says Richard Kautz, a physicist at the US government's National Institute of Standards and Technology in Boulder, Colorado.

Weather is an example of a chaotic system.

This means that the climate has attributes of chaotic system but can not be proven to be actually chaotic.

You said, in post 198: «Therefore climate does have attributes of chaotic system, contrary to what Dan Allan claimed.

As far as surface temperature is concerned — the Royal Society said that climate change is the result of ordered forcing and internal climate variability as a result of climate being an example of a chaotic system.

The property of a chaotic system is that it is not predictible and doesn't follow statistical laws.

Predictions of the future state of a chaotic system, based on wishful thinking, are useful if suckers believe you, and keep giving you money.

It is the nature of a chaotic system.

This is quite a simple concept despite the complexity of the chaotic system.

We can model behavior (space and attractors) but we can not predict the future of any chaotic system.

It is a well known result that when one looks for the right dimensionality of a chaotic system, a minimum of data is necessary.

And if the analysis being undertaken is of a chaotic system then the resulting «trend» has no meaning or value because it has NO predictive power whatsoever.

The fact is as soon as there is any external perturbation of a chaotic system not accounted for in the dynamical equations, you have bumped the system from one path in phase space to another.

Of course, this is the very point Benoit Mandelbrot was trying to get across with the Mandelbrot set — self - similarity can be an emergent property of a chaotic system.

Because you can not apply statistical methods to predict the future of any chaotic system.

Anybody not understanding those facts either do not understand the profound and mostly unknown complexities of the chaotic system or are paid to look the other way.

I do not «believe» in cycles or other such efforts to make sense of a chaotic system.

Indeed the mean state of a chaotic system can be defined by the forcings.

«Indeed the mean state of a chaotic system can be defined by the forcings... forecast with a high degree of confidence that the next month of July will be — on average - warmer than April»

The third assumption is that a fitted curve somehow has magical properties to forecast the evolution of a chaotic system.

Although it is generally not possible to predict a specific future state of a chaotic system (there is no telling what temperature it will be in Oregon on December 21 2012), it is still possible to make statistical claims about the behavior of the system as a whole (it is very likely that Oregon's December 2012 temperatures will be colder than its July 2012 temperatures).

I do think weather and climate clearly chaotic (as per fact, Lorenz and the rest), but I also think the time and effort being put into the forecasting of both suggest a lot of fine minds think useful prediction of this chaotic system possible.

Using models that are optimized for historical accuracy to predict future real states of a chaotic system have error terms that grow as a function of distance from supporting real data.

One of the defining traits of a chaotic system is «sensitive dependence to initial conditions».

Each individual model simulation is like another single realization of the chaotic system.