Related papers: Devaney's chaos revisited
In this study, Devaney's chaos conditions are revisited within the framework of descriptive proximity. The concepts of descriptive transitivity, the density of descriptive periodic objects, and descriptive sensitivity are defined. The most…
This work redefines the framework of chaos in dynamical systems by extending Devaney's definition to multiple mappings, emphasizing the pivotal role of nonlinearity. We propose a novel theorem demonstrating how nonlinear dynamics within a…
We discuss Devaney chaos on compact metric spaces using a decomposition space characterized by topological nature of symbolic dynamics. A chaotic map obtained here is defined as a topologically conjugate of the chaotic map on a…
In this paper, we introduce the definitions of periodic point, transitivity, sensitivity and Devaney chaos of multiple mappings from a set-valued perspective. We study the relation between multiple mappings and its continuous self-maps and…
It is shown that Devaney Chaotic systems have plenty of large periodic points.
This paper introduces a new notion of chaotic algorithms. These algorithms are iterative and are based on so-called chaotic iterations. Contrary to all existing studies on chaotic iterations, we are not interested in stable states of such…
This is a draft paper, proving that the inversion process that occurs in DNA mutations, is indeed chaotic as it is defined by the Devaney's theory.
To prove presence of chaos for fractals, a new mathematical concept of abstract similarity is introduced. As an example, the space of symbolic strings on a finite number of symbols is proved to possess the property. Moreover, Sierpinski…
This is a survey on the recent theory of chaos in partial differential equations.
We give sufficient conditions for sensitivity of continuous group actions on uniform spaces.
It is revealed that a special kind of Poisson stable point, which we call an unpredictable point, gives rise to the existence of chaos in the quasi-minimal set. The existing definitions of chaos are formulated in sets of motions. This is…
The time needed to exchange information in the physical world induces a delay term when the respective system is modeled by differential equations. Time delays are hence ubiquitous, being furthermore likely to induce instabilities and with…
One propounded theory for the presence of chaos in biological neural networks is that it could be involved in discriminating different olfactory stimuli. Inspired by the idea, in this paper, we define the visual ``chaotic perception'' and…
In this article, we show that a chaotic behavior can be found on a cube with arbitrary finite dimension. That is, the cube is a quasi-minimal set with Poincare chaos. Moreover, the dynamics is shown to be Devaney and Li-Yorke chaotic. It…
Chaotic iterations, a tool formerly used in distributed computing, has recently revealed various interesting properties of disorder leading to its use in the computer science security field. In this paper, a comprehensive study of its…
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,…
Numerical analysis indicates that there exists an unexpected new ordered chaos for the bounded one-dimensional multibarrier potential. For certain values of the number of barriers, repeated identical forms (periods) of the wavepackets…
In this paper we consider relations between distributional chaos in a sequence with distributional chaos, w-chaos, R-T chaos, DC 3, respectively). We give a sufficient condition and prove that the distributional chaos is equivalent to the…
We give a more coherent definition of upward planar order.
In the present paper, an essential generalization of the symbolic dynamics is considered. We apply the notions of abstract self-similar sets and the similarity map for a chaos introduction, which orbits are expanded among infinitely many…