相关论文: Distributional chaos and factors

We consider a general N-degree-of-freedom dissipative system which admits of chaotic behaviour. Based on a Fokker-Planck description associated with the dynamics we establish that the drift and the diffusion coefficients can be related…

In a recent Letter [Phys.Rev.Lett., 77,4536 (1996), chao-dyn/9609014] Altland and Zirnbauer claim that they rigorously proved the complete analogy between a (classically chaotic) dynamical system and disordered (random) solids. The purpose…

We investigate dynamics of a jet collimated by magneto-torsional oscillations. The problem is reduced to an ordinary differential equation containing a singularity and depending on a parameter. We find a parameter range for which this…

We report the experimental evidence of the existence of a random attractor in a fully developed turbulent swirling flow. By defining a global observable which tracks the asymmetry in the flux of angular momentum imparted to the flow, we can…

We present a 1-parameter family of systems with fractional monodromy and adiabatic separation of motion. We relate the presence of monodromy to a redistribution of states both in the quantum and semi-quantum spectrum. We show how the…

Hyperchaos is distinguished from chaos by the presence of at least two positive Lyapunov exponents instead of just one in dynamical systems. A general scenario is presented here that shows emergence of hyperchaos with a sudden large…

This paper proves that shadowing solutions can be almost surely nonphysical. This finding invalidates the argument that small perturbations in a chaotic system can only have a small impact on its statistical behavior. This theoretical…

We propose a combination of cluster analysis and stochastic process analysis to characterize high-dimensional complex dynamical systems by few dominating variables. As an example, stock market data are analyzed for which the dynamical…

We observe chaotic dynamics in a damped linear oscillator, which is driven only at certain regions of phase space. Both deterministic and random drives are studied. The dynamics is characterized using standard techniques of nonlinear…

We study numerically statistical distributions of sums of chaotic orbit coordinates, viewed as independent random variables, in weakly chaotic regimes of three multi-dimensional Hamiltonian systems: Two Fermi-Pasta-Ulam (FPU-$\beta$)…

This paper establishes some criteria of chaos in non-autonomous discrete systems. Several criteria of strong Li-Yorke chaos are given. Based on these results, some criteria of distributional chaos in a sequence are established. Moreover,…

This is an easy-to-read introduction to foundations of deterministic chaos, deterministic diffusion and anomalous diffusion. The first part introduces to deterministic chaos in one-dimensional maps in form of Ljapunov exponents and…

A deterministic coalescing dynamics with constant rate for a particle system in a finite volume with a fixed initial number of particles is considered. It is shown that, in the thermodynamic limit, with the constraint of fixed density, the…

In this paper, we give an explicit construction of dynamical systems (defined within a solid torus) containing any knot (or link) and arbitrarily knotted chaos. The first is achieved by expressing the knots in terms of braids, defining a…

In this article we prove that for a diffeomorphism on a compact Riemannian manifold, if there is a nontrival homoclinic class that is not uniformly hyperbolic or the diffeomorphism is a $C^{1+\alpha}$ and there is a hyperbolic ergodic…

We focus on variational inference in dynamical systems where the discrete time transition function (or evolution rule) is modelled by a Gaussian process. The dominant approach so far has been to use a factorised posterior distribution,…

We deal with a mechanism of generating distributional chaos in planar nonautonomous ODEs and try to measure chaosity in terms of topological entropy. It is based on the interplay between simple periodic solutions. We prove the existence of…

A large class of technically non-chaotic systems, involving scatterings of light particles by flat surfaces with sharp boundaries, is nonetheless characterized by complex random looking motion in phase space. For these systems one may…

The efficient detection of chaotic behavior in orbits of a complex dynamical system is an active domain of research. Several indicators have been proposed in the past, and new ones have recently been developed in view of improving the…

A basic model of a dynamical distribution network is considered, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and…