Related papers: A Topological Study of Chaotic Iterations. Applica…

Chaotic itinerancy is a universal dynamical concept that describes itinerant motion among many different ordered states through chaotic transition in dynamical systems. Unlike the expectation of the prevalence of chaotic itinerancy in…

Relationships between a chaotic behavior and closely related properties of topological transitivity, sensitivity to initial conditions, density of closed orbits of homeomorphism groups and their countable products are investigated. We…

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…

We discuss the appearance of chaos in time-periodic perturbations of reversible vector fields in the plane. We use the normal forms of codimension~$1$ reversible vector fields and discuss the ways a time-dependent periodic forcing term of…

Chaos in classical systems has been studied in plenty over many years. Although the search for chaos in quantum systems has been an area of prominent research over the last few decades, the detailed analysis of many inherently chaotic…

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…

ChaosNet is a type of artificial neural network framework developed for classification problems and is influenced by the chaotic property of the human brain. Each neuron of the ChaosNet architecture is the one-dimensional chaotic map called…

The efficient detection of chaotic behavior in orbits of a complex dynamical system is an active domain of research. Several indicators have been proposed in the past, and new ones have recently been developed in view of improving the…

An `obfuscation' for encrypted computing is quantified exactly here, leading to an argument that security against polynomial-time attacks has been achieved for user data via the deliberately `chaotic' compilation required for security…

The emergence of nontrivial collective behavior in networks of coupled chaotic maps is investigated by means of a nonlinear mutual prediction method. The resulting prediction error is used to measure the amount of information that a local…

We undertake a systematic study of the dynamics of Boolean networks to determine the origin of chaos observed in recent experiments. Networks with nodes consisting of ideal logic gates are known to display either steady states, periodic…

The study of experimental data is a relevant task in several physical, chemical and biological applications. In particular, the analysis of chaotic dynamics in cardiac systems is crucial as it can be related to some pathological…

It was recently shown (quant-ph/9909074) that parasitic random interactions between the qubits in a quantum computer can induce quantum chaos and put into question the operability of a quantum computer. In this work I investigate whether…

This paper is the second in a series of two, and describes the current state of the art in modelling and prediction of chaotic time series. Sampled data from deterministic non-linear systems may look stochastic when analysed with linear…

This paper studies the security of a secure communication scheme based on two discrete-time intermittently-chaotic systems synchronized via a common random driving signal. Some security defects of the scheme are revealed: 1) the key space…

When implemented in the digital domain with time, space and value discretized in the binary form, many good dynamical properties of chaotic systems in continuous domain may be degraded or even diminish. To measure the dynamic complexity of…

We study an opto-electronic time-delay oscillator that displays high-speed chaotic behavior with a flat, broad power spectrum. The chaotic state coexists with a linearly-stable fixed point, which, when subjected to a finite-amplitude…

We have found stable chaotic solutions for optomechanical systems coupled with a Two-Level System or qubit. In this system methods have been found which can be used to Tune in and out of Chaos as well as various n-period motions. This…

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…

In this paper, we study the chaotic behavior of a discrete-time linear inclusion.