Quantum network architecture of tight-binding models with substitution sequences

We study a two-spin quantum Turing architecture, in which discrete local rotations \alpha_m of the Turing head spin alternate with quantum controlled NOT-operations. Substitution sequences are known to underlie aperiodic structures. We show that parameter inputs \alpha_m described by such sequences can lead here to a quantum dynamics, intermediate between the regular and the chaotic variant. Exponential parameter sensitivity characterizing chaotic quantum Turing machines turns out to be an adequate criterion for induced quantum chaos in a quantum network.Comment: Accepted for publication in J. mod. Optics [Proc. Workshop "Entanglement and Decoherence", Gargnano (Italy), Sept 1999], 3 figure

Phase transition in a class of non-linear random networks

We discuss the complex dynamics of a non-linear random networks model, as a function of the connectivity k between the elements of the network. We show that this class of networks exhibit an order-chaos phase transition for a critical connectivity k = 2. Also, we show that both, pairwise correlation and complexity measures are maximized in dynamically critical networks. These results are in good agreement with the previously reported studies on random Boolean networks and random threshold networks, and show once again that critical networks provide an optimal coordination of diverse behavior.Comment: 9 pages, 3 figures, revised versio

Families of periodic orbits: Virtual periods and global continuability

AbstractFor a differential equation depending on a parameter, there have been numerous investigations of the continuation of periodic orbits as the parameter is varied. Mallet-Paret and Yorke investigated in generic situations how connected components of orbits must terminate. Here we extend the theory to the general case, dropping genericity assumptions

Dynamical estimates of chaotic systems from Poincar\'e recurrences

We show that the probability distribution function that best fits the distribution of return times between two consecutive visits of a chaotic trajectory to finite size regions in phase space deviates from the exponential statistics by a small power-law term, a term that represents the deterministic manifestation of the dynamics, which can be easily experimentally detected and theoretically estimated. We also provide simpler and faster ways to calculate the positive Lyapunov exponents and the short-term correlation function by either realizing observations of higher probable returns or by calculating the eigenvalues of only one very especial unstable periodic orbit of low-period. Finally, we discuss how our approaches can be used to treat data coming from complex systems.Comment: subm. for publication. Accepted fpr publication in Chao

Bifurcation Phenomena in Two-Dimensional Piecewise Smooth Discontinuous Maps

In recent years the theory of border collision bifurcations has been developed for piecewise smooth maps that are continuous across the border, and has been successfully applied to explain nonsmooth bifurcation phenomena in physical systems. However, many switching dynamical systems have been found to yield two-dimensional piecewise smooth maps that are discontinuous across the border. The theory for understanding the bifurcation phenomena in such systems is not available yet. In this paper we present the first approach to the problem of analysing and classifying the bifurcation phenomena in two-dimensional discontinuous maps, based on a piecewise linear approximation in the neighborhood of the border. We explain the bifurcations occurring in the static VAR compensator used in electrical power systems, using the theory developed in this paper. This theory may be applied similarly to other systems that yield two-dimensional discontinuous maps

Bifurcations in the Lozi map

We study the presence in the Lozi map of a type of abrupt order-to-order and order-to-chaos transitions which are mediated by an attractor made of a continuum of neutrally stable limit cycles, all with the same period.Comment: 17 pages, 12 figure

Delay-Coordinates Embeddings as a Data Mining Tool for Denoising Speech Signals

In this paper we utilize techniques from the theory of non-linear dynamical systems to define a notion of embedding threshold estimators. More specifically we use delay-coordinates embeddings of sets of coefficients of the measured signal (in some chosen frame) as a data mining tool to separate structures that are likely to be generated by signals belonging to some predetermined data set. We describe a particular variation of the embedding threshold estimator implemented in a windowed Fourier frame, and we apply it to speech signals heavily corrupted with the addition of several types of white noise. Our experimental work seems to suggest that, after training on the data sets of interest,these estimators perform well for a variety of white noise processes and noise intensity levels. The method is compared, for the case of Gaussian white noise, to a block thresholding estimator

Chaotic and pseudochaotic attractors of perturbed fractional oscillator

We consider a nonlinear oscillator with fractional derivative of the order alpha. Perturbed by a periodic force, the system exhibits chaotic motion called fractional chaotic attractor (FCA). The FCA is compared to the ``regular'' chaotic attractor. The properties of the FCA are discussed and the ``pseudochaotic'' case is demonstrated.Comment: 20 pages, 7 figure

Time--Evolving Statistics of Chaotic Orbits of Conservative Maps in the Context of the Central Limit Theorem

We study chaotic orbits of conservative low--dimensional maps and present numerical results showing that the probability density functions (pdfs) of the sum of $N$ iterates in the large $N$ limit exhibit very interesting time-evolving statistics. In some cases where the chaotic layers are thin and the (positive) maximal Lyapunov exponent is small, long--lasting quasi--stationary states (QSS) are found, whose pdfs appear to converge to $q$--Gaussians associated with nonextensive statistical mechanics. More generally, however, as $N$ increases, the pdfs describe a sequence of QSS that pass from a $q$--Gaussian to an exponential shape and ultimately tend to a true Gaussian, as orbits diffuse to larger chaotic domains and the phase space dynamics becomes more uniformly ergodic.Comment: 15 pages, 14 figures, accepted for publication as a Regular Paper in the International Journal of Bifurcation and Chaos, on Jun 21, 201

Self-similarities in the frequency-amplitude space of a loss-modulated CO2_2 laser

We show the standard two-level continuous-time model of loss-modulated CO$_2$ lasers to display the same regular network of self-similar stability islands known so far to be typically present only in discrete-time models based on mappings. For class B laser models our results suggest that, more than just convenient surrogates, discrete mappings in fact could be isomorphic to continuous flows.Comment: (5 low-res color figs; for ALL figures high-res PDF: http://www.if.ufrgs.br/~jgallas/jg_papers.html