Related papers: Statistical Distance For Chaotic Maps
While the existing stochastic control theory is well equipped to handle dynamical systems with stochastic uncertainties, a paradigm shift using distance measure based decision making is required for the effective further exploration of the…
The goal of this investigation was to derive strictly new properties of chaotic systems and their mutual relations. The generalized Fokker-Planck equation with a non stationary diffusion has been derived and used for chaos analysis. An…
The aim of this paper is to show how extracting dynamical behavior and ergodic properties from deterministic chaos with the assistance of exact invariant measures. On the one hand, we provide an approach to deal with the inverse problem of…
The phase space of an area-preserving map typically contains infinitely many elliptic islands embedded in a chaotic sea. Orbits near the boundary of a chaotic region have been observed to stick for long times, strongly influencing their…
Concepts from the Ergodic Theory are used to describe the existence of non-transitive maps in attractors of phase synchronous chaotic systems. It is shown that for a class of phase-coherent systems, e.g. the sinusoidally forced Chua's…
Coupled map lattices of weakly coupled Chebychev maps, so-called chaotic strings, may have a profound physical meaning in terms of dynamical models of vacuum fluctuations in stochastically quantized field theories. Here we present analytic…
We show how a recently introduced statistics [Patil et al, Phys. Rev. Lett. 81 5878 (2001)] provides a direct relationship between dimension and predictability in spatiotemporal chaotic systems. Regions of low dimension are identified as…
Quantum steering means that in some bipartite quantum systems, the local measurements on one side can determine the state of the other side. Here we show that in high-dimensional systems, there exists a specific entangled state which can…
This paper introduces a novel motion planning algorithm for stochastic scenarios. We extend the concept of a navigation function to such scenarios. Our main idea is to consider both the Gaussian distribution probabilities of the players'…
A discrete dynamical system in Euclidean m-space generated by the iterates of an asymptotically zero map f, satisfying f(x) goes to zero as x goes to infinity, must have a compact global attracting set $A $. The question of what additional…
In this paper we demonstrate that the phase space arclength of a trajectory, quantified by the time-averaged Lagrangian descriptor, is a robust and self-contained chaos indicator. By invoking Birkhoff's Ergodic Partition Theorem, we show…
The nearest point map of a real algebraic variety with respect to Euclidean distance is an algebraic function. For instance, for varieties of low rank matrices, the Eckart-Young Theorem states that this map is given by the singular value…
We show that there is genuine quantum chaos despite that quantum dynamics is linear. This is revealed by introducing a physical distance between two quantum states. Qualitatively different from existing distances for quantum states, for…
Recurrence in the phase space of complex systems is a well-studied phenomenon, which has provided deep insights into the nonlinear dynamics of such systems. For dissipative systems, characteristics based on recurrence plots have recently…
Temporal graphs are commonly used to represent time-resolved relations between entities in many natural and artificial systems. Many techniques were devised to investigate the evolution of temporal graphs by comparing their state at…
The standard approach to characterizing topological matter, computing topological invariants, fails when the symmetry protecting the topological phase is preserved only on average in a disordered system. Because topological invariants rely…
Geometry and topology have generated impacts far beyond their pure mathematical primitive, providing a solid foundation for many applicable tools. Typically, real-world data are represented as vectors, forming a linear subspace for a given…
In this paper we analyze chaotic dynamics for two dimensional nonautonomous maps through the use of a nonautonomous version of the Conley-Moser conditions given previously. With this approach we are able to give a precise definition of what…
in the last decade, studies of chaotic system are more often used for classical choatic system than for quantum chaotic system, there are many ways of observing the chaotic system such us analyzing the frequency with Fourier transform or…
We study a stochastically-driven standard map. The addition of a noise term destroys the invariant manifolds that organize the phase space which allows for more widespread transport than in the noiseless case. Using appropriately defined…