Related papers: Chaotic singular maps
We describe a simple adaptive network of coupled chaotic maps. The network reaches a stationary state (frozen topology) for all values of the coupling parameter, although the dynamics of the maps at the nodes of the network can be…
The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…
A new type of deterministic chaos for a system described by iterative two-dimensional maps is reported. The series being generated by the original map has an average upward trend while the first difference, which is the series of changes…
Piecewise-linear maps describe dynamical phenomena that switch between distinct states and readily generate complex bifurcation structures due to their strong nonlinearity. We show that two-dimensional continuous piecewise-linear maps near…
The paper is focused on the discussion of the phenomenon of transitional chaos in dynamic autonomous and non-autonomous systems. This phenomenon involves the disappearance of chaotic oscillations in specific time periods and the system…
In this paper, we introduce a hybrid chaos map for image encryption method with high sensitivity. This new map is sensitive to small changes in the starting point and also in control parameters which result in having more computational…
Intermittent dynamics is characterized by long periods of different types of dynamical characteristics, for instance almost periodic dynamics alternated by chaotic dynamics. Critical intermittency is intermittent dynamics that can occur in…
The defining feature of chaos is its hypersensitivity to small perturbations. However, we report a stability of branched flow against large perturbations where the classical trajectories are chaotic, showing that strong perturbations are…
This paper presents a more complete version than hitherto published of our explanation of a transition from regular to irregular motions and more generally of the nature of a certain kind of deterministic chaos. To this end we introduced a…
We show that the output of systems with time-varying delay can exhibit a new kind of chaotic behavior characterized by laminar phases, which are periodically interrupted by irregular bursts. Within each laminar phase the output intensity…
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…
Classical chaos is marked by an extreme sensitivity to initial conditions, where infinitesimally close trajectories separate exponentially over time. In quantum mechanics, however, unitary evolution and the uncertainty principle preclude…
We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…
In order to analyze the effect of chaos or order on the rate of decoherence in a subsystem we aim to distinguish effects of the two types of dynamics from those depending on the choice of the wave packet. To isolate the former we introduce…
We give a qualitative description of two main routes to chaos in three-dimensional maps. We discuss Shilnikov scenario of transition to spiral chaos and a scenario of transition to discrete Lorenz-like and figure-eight strange attractors.…
The paper considers a stabilizing stochastic control which can be applied to a variety of unstable and even chaotic maps. Compared to previous methods introducing control by noise, we relax assumptions on the class of maps, as well as…
Digital implementations of chaotic systems often suffer from inherent degradation, limiting their long-term performance and statistical quality. To address this challenge, we propose a novel four-stage synchronized piecewise linear chaotic…
We show that dynamical clustering, where a system segregates into distinguishable subsets of synchronized elements, and chimera states, where differentiated subsets of synchronized and desynchronized elements coexist, can emerge in networks…
Modern space missions with uncrewed spacecraft require robust trajectory design to connect multiple chaotic orbits by small controls. To address this issue, we propose a control scheme to design robust trajectories by leveraging a…
In this paper, we consider a class of continuous maps characterized by a singularity of order $x^{q/p}$ (with $p,q \in \mathbb{N}$, $p>q$, and $(p,q)=1$) on one side of the discontinuity boundary $\Sigma$ and a linear behaviour on the other…