Related papers: Distributional Chaos in Random Dynamical Systems
We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check,…
Non-deterministic chaos is a form of low-dimensional dynamics which is characterized by the existence of a countable set of {\em sensitive decision points} (SDP's). Away from these points, the dynamics is well-behaved. Near these points,…
We introduce a new analytical method, which allows to find out chaotic dynamics in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered as an example. The corresponding…
We show the existence of a dynamical system without any distributionally scrambled pair which is semiconjugated to a distributionally chaotic factor.
Dynamical systems on the interval were widely studied because they are among the simplest systems and nevertheless they turn out to have complex dynamics. Many works on chaos were inspired by the behaviour of interval maps. However these…
The paper deals with the theoretical analysis of a logistic system composed of at least two elements with distributed parameters. It has been shown that such a system may generate specific oscillations in spite of the fact that the…
In this expository and resources chapter we review selected aspects of the mathematics of dynamical systems, stability, and chaos, within a historical framework that draws together two threads of its early development: celestial mechanics…
We consider the distribution of the (properly normalized) numbers of nodal domains of wave functions in 2-$d$ quantum billiards. We show that these distributions distinguish clearly between systems with integrable (separable) or chaotic…
We confront existing definitions of chaos with the state of the art in topological dynamics. The article does not propose any new definition of chaos but, starting from several topological properties that can be reasonably called chaotic,…
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…
What is chaos? Despite several decades of research on this ubiquitous and fundamental phenomenon there is yet no agreed-upon answer to this question. Recently, it was realized that all stochastic and deterministic differential equations,…
We investigate the connections between microscopic chaos, defined on a dynamical level and arising from collisions between molecules, and diffusion, characterized by a mean square displacement proportional to the time. We use a number of…
The full family of discrete logistic maps has been widely studied both as a canonical example of the period-doubling route to chaos, and as a model of natural processes. In this paper we present a study of the stochastic process described…
We review application of level dynamics to spectra of quantally chaotic systems. We show that statistical mechanics approach gives us predictions about level statistics intermediate between integrable and chaotic dynamics. Then we discuss…
The research concerns the dynamics of complex autonomous Kauffman networks. The article defines and shows using simulation experiments half-chaotic networks, which exhibit features much more similar to typically modeled systems like a…
In this paper, a nonlinear system aiming at reducing the signal transmission rate in a networked control system is constructed by adding nonlinear constraints to a linear feedback control system. Its stability is investigated in detail. It…
For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a…
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…
The transient chaos regime in a two-dimensional system with discrete time (Eno map) is considered. It is demonstrated that a time series corresponding to this regime differs from a chaotic series constructed for close values of the control…
Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be…