Related papers: On distributional chaos in non-autonomous discrete…
If a topological dynamical system $(X,T)$ has positive topological entropy, then it is multivariant mean Li-Yorke chaotic along a sequence $\{a_k\}_{k=1}^\infty$ of positive integers which is "good" for pointwise ergodic convergence with a…
In recent years, a lot of research has gone into creating multi-layer chaotic mapping-based cryptosystems. Random-like behavior, a continuous broadband power spectrum, and a weak baseline condition dependency are all characteristics of…
We study synchronization of non-diffusively coupled map networks with arbitrary network topologies, where the connections between different units are, in general, not symmetric and can carry both positive and negative weights. We show that,…
The stationary distributions of sums of positions of trajectories generated by the logistic map have been found to follow a basic renormalization group (RG) structure: a nontrivial fixed-point multi-scale distribution at the period-doubling…
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…
A new type of chaos called laminar chaos was found in singularly perturbed dynamical systems with periodic time-varying delay [Phys. Rev. Lett. 120, 084102 (2018)]. It is characterized by nearly constant laminar phases, which are…
We characterize dendrites $D$ such that a continuous selfmap of $D$ is generically chaotic (in the sense of Lasota) if and only if it is generically $\varepsilon$-chaotic for some $\varepsilon>0$. In other words, we characterize dendrites…
Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science.…
This article investigates the relation between the distributional chaos and the existence of a scrambled triple. We show that for a continuous mapping $f$ acting on a compact metric space $(X,d)$, the possession of an infinite extremal…
Recent progress toward classifying low-dimensional chaos measured from time series data is described. This classification theory assigns a template to the time series once the time series is embedded in three dimensions. The template…
Motivated by C*-algebra theory, ultragraph edge shift spaces generalize shifts of finite type to the infinite alphabet case. In this paper we study several notions of chaos for ultragraph shift spaces. More specifically, we show that…
This paper establishes topological (equi-)semiconjugacy and (equi-)conjugacy between induced non-autonomous set-valued systems and subshifts of finite type. First, some necessary and sufficient conditions are given for a non-autonomous…
Chaos as typical property of non-linear systems has revealed its crucial role in various problems of astrophysics and cosmology. The problems discussed at these lectures include planetary dynamics, galactic dynamics, reconstruction of the…
Collective behavior is studied in globally coupled maps with distributed nonlinearity. It is shown that the heterogeneity enhances regularity in the collective dynamics. Low-dimensional quasiperiodic motion is often found for the…
There are lots of results to study dynamical complexity on irregular sets and level sets of ergodic average from the perspective of density in base space, Hausdorff dimension, Lebesgue positive measure, positive or full topological entropy…
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…
The concept of "$A$-coupled-expanding" map for a transition matrix $A$ has been studied as one of the most important criteria of chaos in the past years. In this paper, the lower bound of the topological entropy for strictly…
We show that a linear quantum harmonic oscillator is chaotic in the sense of Li-Yorke. We also prove that the weighted backward shift map, used as an infinite dimensional linear chaos model, in a separable Hilbert space is chaotic in the…
The Chirikov resonance-overlap criterion predicts the onset of global chaos if nonlinear resonances overlap in energy, which is conventionally assumed to require a non-small magnitude of perturbation. We show that, for a time-periodic…
We answer the two questions left open in [Z.~Ko\v{c}an, Internat. J. Bifur. Chaos Appl. Sci. Engrg. \textbf{22}, article id: 125025 (2012)] i.e. whether there is a relation between $\omega$-chaos and distributional chaos and whether there…