Strange attractor in optical logic cells

Optical logic cells, employed in several tasks as optical computing or optically controlled switches for photonic switching, offer a very particular behavior when the working conditions are slightly modified. One of the more striking changes occurs when some delayed feedback is applied between one of the possible output gates and a control input. Some of these new phenomena have been studied by us and reported in previous papers. A chaotic behavior is one of the more characteristic results and its possible applications range from communications to cryptography. But the main problem related with this behavior is the binary character of the resulting signal. Most of the nowadays-employed techniques to analyze chaotic signals concern to analogue signals where algebraic equations are possible to obtain. There are no specific tools to study digital chaotic signals. Some methods have been proposed. One of the more used is equivalent to the phase diagram in analogue chaos. The binary signal is converted to hexadecimal and then analyzed. We represented the fractal characteristics of the signal. It has the characteristics of a strange attractor and gives more information than the obtained from previous methods. A phase diagram, as the one obtained by previous techniques, may fully cover its surface with the trajectories and almost no information may be obtained from it. Now, this new method offers the evolution around just a certain area being this lines the strange attractor.

Estimating Attractor Dimension on the Nonlinear Pendulum Time Series

Chaotic dynamical systems exhibit trajectories in their phase space that converges to a strange attractor. The strangeness of the chaotic attractor is associated with its dimension in which instance it is described by a noninteger dimension. This contribution presents an overview of the main definitions of dimension discussing their evaluation from time series employing the correlation and the generalized dimension. The investigation is applied to the nonlinear pendulum where signals are generated by numerical integration of the mathematical model, selecting a single variable of the system as a time series. In order to simulate experimental data sets, a random noise is introduced in the time series. State space reconstruction and the determination of attractor dimensions are carried out regarding periodic and chaotic signals. Results obtained from time series analyses are compared with a reference value obtained from the analysis of mathematical model, estimating noise sensitivity. This procedure allows one to identify the best techniques to be applied in the analysis of experimental data.

Topological entropy of catalytic sets: Hypercycles revisited

The dynamics of catalytic networks have been widely studied over the last decades because of their implications in several fields like prebiotic evolution, virology, neural networks, immunology or ecology. One of the most studied mathematical bodies for catalytic networks was initially formulated in the context of prebiotic evolution, by means of the hypercycle theory. The hypercycle is a set of self-replicating species able to catalyze other replicator species within a cyclic architecture. Hypercyclic organization might arise from a quasispecies as a way to increase the informational containt surpassing the so-called error threshold. The catalytic coupling between replicators makes all the species to behave like a single and coherent evolutionary multimolecular unit. The inherent nonlinearities of catalytic interactions are responsible for the emergence of several types of dynamics, among them, chaos. In this article we begin with a brief review of the hypercycle theory focusing on its evolutionary implications as well as on different dynamics associated to different types of small catalytic networks. Then we study the properties of chaotic hypercycles with error-prone replication with symbolic dynamics theory, characterizing, by means of the theory of topological Markov chains, the topological entropy and the periods of the orbits of unimodal-like iterated maps obtained from the strange attractor. We will focus our study on some key parameters responsible for the structure of the catalytic network: mutation rates, autocatalytic and cross-catalytic interactions.

Organisational Values as "Attractors of Chaos": An Emerging Cultural Change to Manage Organisational Complexity

Business organisations are excellent representations of what in physics and mathematics are designated "chaotic" systems. Because a culture of innovation will be vital for organisational survival in the 21st century, the present paper proposes that viewing organisations in terms of "complexity theory" may assist leaders in fine-tuning managerial philosophies that provide orderly management emphasizing stability within a culture of organised chaos, for it is on the "boundary of chaos" that the greatest creativity occurs. It is argued that 21st century companies, as chaotic social systems, will no longer be effectively managed by rigid objectives (MBO) nor by instructions (MBI). Their capacity for self-organisation will be derived essentially from how their members accept a shared set of values or principles for action (MBV). Complexity theory deals with systems that show complex structures in time or space, often hiding simple deterministic rules. This theory holds that once these rules are found, it is possible to make effective predictions and even to control the apparent complexity. The state of chaos that self-organises, thanks to the appearance of the "strange attractor", is the ideal basis for creativity and innovation in the company. In this self-organised state of chaos, members are not confined to narrow roles, and gradually develop their capacity for differentiation and relationships, growing continuously toward their maximum potential contribution to the efficiency of the organisation. In this way, values act as organisers or "attractors" of disorder, which in the theory of chaos are equations represented by unusually regular geometric configurations that predict the long-term behaviour of complex systems. In business organisations (as in all kinds of social systems) the starting principles end up as the final principles in the long term. An attractor is a model representation of the behavioral results of a system. The attractor is not a force of attraction or a goal-oriented presence in the system; it simply depicts where the system is headed based on its rules of motion. Thus, in a culture that cultivates or shares values of autonomy, responsibility, independence, innovation, creativity, and proaction, the risk of short-term chaos is mitigated by an overall long-term sense of direction. A more suitable approach to manage the internal and external complexities that organisations are currently confronting is to alter their dominant culture under the principles of MBV.

Organisational values as "attractors of chaos": An emerging cultural change to manage organisational complexity

Business organisations are excellent representations of what in physics and mathematics are designated "chaotic" systems. Because a culture of innovation will be vital for organisational survival in the 21st century, the present paper proposes that viewing organisations in terms of "complexity theory" may assist leaders in fine-tuning managerial philosophies that provide orderly management emphasizing stability within a culture of organised chaos, for it is on the "boundary of chaos" that the greatest creativity occurs. It is argued that 21st century companies, as chaotic social systems, will no longer be effectively managed by rigid objectives (MBO) nor by instructions (MBI). Their capacity for self-organisation will be derived essentially from how their members accept a shared set of values or principles for action (MBV). Complexity theory deals with systems that show complex structures in time or space, often hiding simple deterministic rules. This theory holds that once these rules are found, it is possible to make effective predictions and even to control the apparent complexity. The state of chaos that self-organises, thanks to the appearance of the "strange attractor", is the ideal basis for creativity and innovation in the company. In this self-organised state of chaos, members are not confined to narrow roles, and gradually develop their capacity for differentiation and relationships, growing continuously toward their maximum potential contribution to the efficiency of the organisation. In this way, values act as organisers or "attractors" of disorder, which in the theory of chaos are equations represented by unusually regular geometric configurations that predict the long-term behaviour of complex systems. In business organisations (as in all kinds of social systems) the starting principles end up as the final principles in the long term. An attractor is a model representation of the behavioral results of a system. The attractor is not a force of attraction or a goal-oriented presence in the system; it simply depicts where the system is headed based on its rules of motion. Thus, in a culture that cultivates or shares values of autonomy, responsibility, independence, innovation, creativity, and proaction, the risk of short-term chaos is mitigated by an overall long-term sense of direction. A more suitable approach to manage the internal and external complexities that organisations are currently confronting is to alter their dominant culture under the principles of MBV.

Global dynamics of the Rikitake system

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the global dynamics of the Rabinovich system

In this paper by using the Poincare compactification in R(3) make a global analysis of the Rabinovich system(x) over dot = hy - v(1)x + yz, (y) over dot = hx - v(2)y - xz, (z) over dot = -v(3)z + xy,with (x, y, z) is an element of R(3) and ( h, v(1), v(2), v(3)) is an element of R(4). We give the complete description of its dynamics on the sphere at infinity. For ten sets of the parameter values the system has either first integrals or invariants. For these ten sets we provide the global phase portrait of the Rabinovich system in the Poincare ball (i.e. in the compactification of R(3) with the sphere S(2) of the infinity). We prove that for convenient values of the parameters the system has two families of singularly degenerate heteroclinic cycles. Then changing slightly the parameters we numerically found a four wings butterfly shaped strange attractor.

Transition to turbulence in the Reynolds' experiment

In this study we simulate numerically the Reynolds' experiment for the transition from laminar to turbulent flow in a pipe. We present a discussion of the results from a dynamical systems perspective when a control parameter, the Reynolds number, is increased. The Landau scenario, where the transition is described by the excitation of infinite oscillatory modes within the fluid, is not observed. Instead what happens is best explained by the Ruelle-Takens scenario in terms of strange attractors. The Lyapunov exponent and fractal dimension for the attractor are calculated together with a measure of complex behaviour called the Lempel-Ziv complexity. (C) 2001 Elsevier B.V. B.V. All rights reserved.

A teoria da complexidade na aprendizagem de espanhol em Teletandem

Pós-graduação em Estudos Linguísticos - IBILCE

Characterizing chaos in a type of fractional duffing's equation

We characterize the chaos in a fractional Duffing’s equation computing the Lyapunov exponents and the dimension of the strange attractor in the effective phase space of the system. We develop a specific analytical method to estimate all Lyapunov exponents and check the results with the fiduciary orbit technique and a time series estimation method.

Strange nonchaotic attractors in Harper maps

We study the existence of strange nonchaotic attractors (SNA) in the family of Harper maps. We prove that for a set of parameters of positive measure, the map possesses a SNA. However, the set is nowhere dense. By changing the parameter arbitrarily small amounts, the attractor is a smooth curve and not a SNA.

Spiral attractor created by vector solitons

Mode-locked lasers emitting a train of femtosecond pulses called dissipative solitons are an enabling technology for metrology, high-resolution spectroscopy, fibre optic communications, nano-optics and many other fields of science and applications. Recently, the vector nature of dissipative solitons has been exploited to demonstrate mode locked lasing with both locked and rapidly evolving states of polarisation. Here, for an erbium-doped fibre laser mode locked with carbon nanotubes, we demonstrate the first experimental and theoretical evidence of a new class of slowly evolving vector solitons characterized by a double-scroll chaotic polarisation attractor substantially different from Lorenz, Rössler and Ikeda strange attractors. The underlying physics comprises a long time scale coherent coupling of two polarisation modes. The observed phenomena, apart from the fundamental interest, provide a base for advances in secure communications, trapping and manipulation of atoms and nanoparticles, control of magnetisation in data storage devices and many other areas. © 2014 CIOMP. All rights reserved.

Centrality dependence of charged hadron and strange hadron elliptic flow from root s(NN)=200 GeVAu+Au collisions

We present STAR results on the elliptic flow upsilon(2) Of charged hadrons, strange and multistrange particles from,root s(NN) = 200 GeV Au+Au collisions at the BNL Relativistic Heavy Ion Collider (RHIC). The detailed study of the centrality dependence of upsilon(2) over a broad transverse momentum range is presented. Comparisons of different analysis methods are made in order to estimate systematic uncertainties. To discuss the nonflow effect, we have performed the first analysis Of upsilon(2) with the Lee-Yang zero method for K(S)(0) and A. In the relatively low PT region, P(T) <= 2 GeV/c, a scaling with m(T) - m is observed for identified hadrons in each centrality bin studied. However, we do not observe nu 2(p(T))) scaled by the participant eccentricity to be independent of centrality. At higher PT, 2 1 <= PT <= 6 GeV/c, V2 scales with quark number for all hadrons studied. For the multistrange hadron Omega, which does not suffer appreciable hadronic interactions, the values of upsilon(2) are consistent with both m(T) - m scaling at low p(T) and number-of-quark scaling at intermediate p(T). As a function ofcollision centrality, an increase of p(T)-integrated upsilon(2) scaled by the participant eccentricity has been observed, indicating a stronger collective flow in more central Au+Au collisions.

Enhanced strange baryon production in Au+Au collisions compared to p+p at root s(NN)=200 GeV

We report on the observed differences in production rates of strange and multistrange baryons in Au+Au collisions at s(NN)=200 GeV compared to p+p interactions at the same energy. The strange baryon yields in Au+Au collisions, when scaled down by the number of participating nucleons, are enhanced relative to those measured in p+p reactions. The enhancement observed increases with the strangeness content of the baryon, and it increases for all strange baryons with collision centrality. The enhancement is qualitatively similar to that observed at the lower collision energy s(NN)=17.3 GeV. The previous observations are for the bulk production, while at intermediate p(T),1 < p(T)< 4 GeV/c, the strange baryons even exceed binary scaling from p+p yields.

Color-flavor locked strange matter and strangelets at finite temperature

It is possible that a system composed of up, down, and strange quarks exists as the true ground state of nuclear matter at high densities and low temperatures. This exotic plasma, called strange quark matter (SQM), seems to be even more favorable energetically if quarks are in a superconducting state, the so-called color-flavor locked state. Here we present calculations made on the basis of the MIT bag model, considering the influence of finite temperature on the allowed parameters characterizing the system for stability of bulk SQM (the so-called stability windows) and also for strangelets, small lumps of SQM, both in the color-flavor locking scenario. We compare these results with the unpaired SQM and also briefly discuss some astrophysical implications of them. Also, the issue of the strangelet's electric charge is discussed. The effects of dynamical screening, though important for nonpaired SQM strangelets, are not relevant when considering pairing among all three flavors and colors of quarks.