Related papers: Chaotic singular maps
We investigate the long-term diffusion transport and chaos properties of single and coupled standard maps. We consider model parameters that are known to induce anomalous diffusion in the maps' phase spaces, as opposed to normal diffusion…
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…
Based on newly discovered properties of the shift map (Theorem 1), we believe that chaos should involve not only nearby points can diverge apart but also faraway points can get close to each other. Therefore, we propose to call a continuous…
In recent years, a growing number of cryptosystems based on chaos have been proposed. But most of them encountered many problems such as small key space and weak security. In the present paper, a new kind of chaotic cryptosystem based on…
Experiments observing the liquid surface in a vertically oscillating container have indicated that modeling the dynamics of such systems require maps that admit states at infinity. In this paper we investigate the bifurcations in such a…
Transport in Hamiltonian systems with weak chaotic perturbations has been much studied in the past. In this paper, we introduce a new class of problems: transport in Hamiltonian systems with slowly changing phase space structure that are…
Complexity of dynamical networks can arise not only from the complexity of the topological structure but also from the time evolution of the topology. In this paper, we study the synchronous motion of coupled maps in time-varying complex…
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…
We study raw coding of trajectories of a chaotic dynamical system by sequences of elements from a finite alphabet and show that there is a fundamental constraint on differences between codes corresponding to different trajectories of the…
The idea that chaos could be a useful tool for analyze nonlinear systems considered in this paper and for the first time the two time scale property of singularly perturbed systems is analyzed on chaotic attractor. The general idea…
Chaotic behavior arises from very simple non-linear dynamical equation of logistic map which makes it was used often in designing chaotic image encryption schemes. However, some properties of chaotic maps can also facilitate cryptanalysis…
Continuous-time systems with switch-like behaviour occur in chemical kinetics, gene regulatory networks and neural networks. Networks with hard switching, as a limiting case of smooth sigmoidal switching, retain the richest possible range…
Chaotic maps are very important for establishing chaos-based image encryption systems. This paper introduces a coupling chaotic system based on a certain unit transform, which can combine any two 1D chaotic maps to generate a new one with…
We present a number of second order maps, which pass the singularity confinement test commonly used to identify integrable discrete systems, but which nevertheless are non-integrable. As a more sensitive integrability test, we propose the…
Dynamical networks are important models for the behaviour of complex systems, modelling physical, biological and societal systems, including the brain, food webs, epidemic disease in populations, power grids and many other. Such dynamical…
The paper gives a systematic analysis of singularities of transition processes in dynamical systems. General dynamical systems with dependence on parameter are studied. A system of relaxation times is constructed. Each relaxation time…
In this paper we investigate a fractional order logistic map and its discrete time dynamics. We show some basic properties of the fractional logistic map and numerically study its period-doubling route to chaos.
Depending on initial conditions, individual finite time trajectories of dynamical systems can have very different chaotic properties. Here we present a numerical method to identify trajectories with atypical chaoticity, pathways that are…
In shear flows like pipe flow and plane Couette flow there is an extended range of parameters where linearly stable laminar flow coexists with a transient turbulent dynamics. When increasing the amplitude of a perturbation on top of the…
In this paper we introduce some weak dynamical properties by using subbases for the phase space. Among them, the notion of light chaos is the most significant. Severalexamples, which clarify the relationships between this kind of chaos and…