Related papers: Dendrites and chaos
In this paper, various chaotic properties and their relationships for interval maps are discussed. It is shown that the proximal relation is an equivalence relation for any zero entropy interval map. The structure of the set of…
We consider a disordered system obtained by coupling two mixed even-spin models together. The chaos problem is concerned with the behavior of the coupled system when the external parameters in the two models, such as, temperature, disorder,…
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…
In this paper, we investigate the distributional chaos of the composition operator $T_{\varphi}:f\mapsto f\circ\varphi$ on $L^{p}(X,\mathcal{B},\mu)$, $1\leq p <\infty$. We provide a characterization and practical sufficient conditions on…
We study chaotic properties of uniformly convergent nonautonomous dynamical systems. We show that, contrary to the autonomous systems on the compact interval, positivity of topological sequence entropy and occurrence of Li-Yorke chaos are…
Periodicity plays a significant role in the chaos theory from the beginning since the skeleton of chaos can consist of infinitely many unstable periodic motions. This is true for chaos in the sense of Devaney [1], Li-Yorke [2] and the one…
The relevance of chaos to evolution is discussed in the context of the origin and maintenance of diversity and complexity. Evolution to the edge of chaos is demonstrated in an imitation game. As an origin of diversity, dynamic clustering of…
In many applications, there is a desire to determine if the dynamics of interest are chaotic or not. Since positive Lyapunov exponents are a signature for chaos, they are often used to determine this. Reliable estimates of Lyapunov…
We derive lower bounds for the variance of the difference of energies between incongruent ground states, i.e., states with edge overlaps strictly less than one, of the Edwards-Anderson model on ${\mathbb Z}^d$. The bounds highlight a…
We discuss the relation between Devaney chaos in the base system and Devaney chaos in its induced hyperspace system. We show that the latter need not imply the former. We also argue that this implication is not true even in the strengthened…
We study the quantum Lyapunov exponent $\lambda_L$ in theories with spacetime-independent disorder. We first derive self-consistency equations for the two- and four-point functions for products of $N$ models coupled by disorder at large…
In this paper, we introduce the notion of distributional chaos and the measure of chaos for random dynamical systems generated by two interval maps. We give some sufficient conditions for a zero measure of chaos and examples of chaotic…
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 authors present two results on infinite-dimensional linear dynamical systems with chaoticity. One is about the chaoticity of the backward shift map in the space of infinite sequences on a general Fr\'{e}chet space. The other is about…
We argue that Gaspard and coworkers [Nature 394, 865 (1998)] do not give evidence for microscopic chaos in the sense in which they use the term. The effectively infinite number of molecules in a fluid can generate the same macroscopic…
Dynamical chaos is a term that encompasses a wide range of nonlinear phenomena such as turbulence, neuronal avalanches, weather patterns, and many others. However, despite much work in the field of chaos, its fundamental physical origin…
In this paper we consider the question of distributional chaos on non-compact metric dynamical systems. We focus on a shift space over a countable alphabet, the Baire Space. We prove that on the Baire Space subshifts of finite type exhibit…
In recent years, the topic of car-following has experimented an increased importance in traffic engineering and safety research. This has become a very interesting topic because of the development of driverless cars…
Quantized, compact graphs were shown to be excellent paradigms for quantum chaos in bounded systems. Connecting them with leads to infinity we show that they display all the features which characterize scattering systems with an underlying…
The problem of Turing pattern formation has attracted much attention in nonlinear science as well as physics, chemistry and biology. So far all Turing patterns have been observed in stationary and oscillatory media only. In this letter we…