Related papers: Chaotic principle: an experimental test
We describe a way of interpreting the chaotic principle of (ref. [GC1]) more extensively than it was meant in the original works. Mathematically the analysis is based on the dynamical notions of Axiom A and Axiom B and on the notion of…
A chaotic system under periodic forcing can develop a periodically visited strange attractor. We discuss simple models in which the phenomenon, quite easy to see in numerical simulations, can be completely studied analytically.
In many real world chaotic systems, the interest is typically in determining when the system will behave in an extreme manner. Flooding and drought, extreme heatwaves, large earthquakes, and large drops in the stock market are examples of…
The chaotic hypothesis has several implications which have generated interest in the literature because of their generality and because a few exact predictions are among them. However its application to Physics problems requires attention…
From the climate system to the effect of the internet on society, chaotic systems appear to have a significant role in our future. Here a method of statistical learning for a class of chaotic systems is described along with underlying…
Starting from Anosov chaotic dynamics of geodesic flow on a surface of negative curvature, we develop and consider a number of self-oscillatory systems including those with hinged mechanical coupling of three rotators and a system of…
In this paper we present a general result with an easily checkable condition that ensures a transition from chaotic regime to regular regime in random dynamical systems with additive noise. We show how this result applies to a prototypical…
The main theorem of this paper establishes conditions under which the "chaos game" algorithm almost surely yields the attractor of an iterated function system. The theorem holds in a very general setting, even for non contractive iterated…
Chaotic systems arise naturally in Statistical Mechanics and in Fluid Dynamics. A paradigm for their modelization are smooth hyperbolic systems. Are there consequences that can be drawn simply by assuming that a system is hyperbolic? here…
The character of the time-asymptotic evolution of physical systems can have complex, singular behavior with variation of a system parameter, particularly when chaos is involved. A perturbation of the parameter by a small amount $\epsilon$…
A simple class of chaotic systems in a random environment is considered and the fluctuation theorem is extended under the assumption of reversibility.
Recently it has been found that different physical systems driven by identical random noise behave exactly identical after a long time. It is also suggested that this is an outcome of finite precision in numerical experiments. Here we show…
The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying…
Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by…
We evoke the idea of representation of the chaotic attractor by the set of unstable periodic orbits and disclose a novel noise-induced ordering phenomenon. For long unstable periodic orbits forming the strange attractor the weights (or…
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene…
Chaos control techniques have been applied to a wide variety of experimental systems, including magneto-elastic ribbons, lasers, chemical reactions, arrhythmic cardiac tissue, and spontaneously bursting neuronal networks. An underlying…
The influence of noise on the generalized synchronization regime in the chaotic systems with dissipative coupling is considered. If attractors of the drive and response systems have an infinitely large basin of attraction, generalized…
The chaotic hypothesis is proposed as a basis for a general theory of nonequilibrium stationary states. Version 2: new comments added after presenting this talk at the Meeting mentioned in the Acknowledgement. One typo corrected.
The chaotic properties of simple two-dimensional rotation-translation models are explored and simulated. The models are given in difference equation forms, while the corresponding differential equations systems are studied and the resulting…