Abstract:
Este trabalho tem por objetivo apresentar um modelo teórico simplificado de cadeia produtiva onde as rela es entre o número de competidores, os tempos de resposta para ajustes da produ o e a intensidade da resposta das empresas levam intrinsecamente ao surgimento de oscila es caóticas na oferta e na demanda. No modelo proposto, desenvolvido com o uso da metodologia de dinamica de sistemas, as flutua es irregulares na demanda e nos pre os est o intimamente relacionadas com a própria estrutura da cadeia, ou seja, com suas regras, políticas e capacidades produtivas. S o feitas considera es sobre a importancia do estudo de caos aplicado à economia e s o discutidas técnicas para caracteriza o de comportamento caótico em séries econ micas. The purpose of this study was to present a simplified supply chain model where the relations between the number of competitors, the delay in production adjustments, and the intensity response of each company lead, intrinsically, to the emergence of chaotic oscillations in supply and demand. In the considered model, developed with the use of the System Dynamics methodology, the irregular fluctuations in demand and prices are closely related to the supply chain structure, that is, its rules, policies and capabilities. Discussions about the importance of the study of chaos applied to the economy are developed and specific techniques for characterization of chaotic behavior in economic time series are presented.

Abstract:
We examine the radioactive decay of iodine in terms of its Kolmogorov entropy, observing a consistency with the presence of a regime of deterministic chaos in the vacuum dynamics.

Abstract:
Non-deterministic chaos is a new dynamical paradigm where a non-deterministic system is influenced by random perturbations to produce the appearance of complexity. The non-determinism is envisioned to occur only at a single point in phase space, where many trajectories intersect. In the presence of external random perturbations (noise), whenever the phase space trajectory approaches the singularity, it will jump in an unpredictable way to a different solution. This behavior, while similar in appearance to deterministic chaos, has rather different implications for prediction and control.

Abstract:
Non-deterministic chaos is a form of low-dimensional dynamics which is characterized by the existence of a countable set of {\em sensitive decision points} (SDP's). Away from these points, the dynamics is well-behaved. Near these points, however, perturbations (e.g., thermal noise) may cause the outgoing trajectory to be chosen randomly. An example of a non-deterministic chaotic system is given, and a statistical method of analyzing the resultant dynamics is developed.

Abstract:
This is an easy-to-read introduction to foundations of deterministic chaos, deterministic diffusion and anomalous diffusion. The first part introduces to deterministic chaos in one-dimensional maps in form of Ljapunov exponents and dynamical entropies. The second part outlines the concept of deterministic diffusion. Then the escape rate formalism for deterministic diffusion, which expresses the diffusion coefficient in terms of the above two chaos quantities, is worked out for a simple map. Part three explains basics of anomalous diffusion by demonstrating the stochastic approach of continuous time random walk theory for an intermittent map. As an example of experimental applications, the anomalous dynamics of biological cell migration is discussed.

Abstract:
We discuss the necessity and demonstrate the validity of introduction the notion of deterministic chaos in quantum field theory. Brief review of the existing approaches to this problem is given. We compare proposed chaos criterion for quantum fields with existing ones. Its consequences in particle physics are also discussed.

Abstract:
Although it is often assumed that the southern African systems of misfortune interpretation are deterministic, the notion of deterministic chaos seems to be more accurate to understand underlying principles of the Mozambican divination with tinhlolo. That system is based on a deterministic structure, it seeks to explain and to regulate the uncertainty, but its outcome is chaotic due to the complexity of the factors involved, unknowable in their totality and characterised by agency. To understand it as a domestication of aleatory system legitimates new comparison fields worldwide (including with the probabilistic notion of "risk"), and refocuses the study of Ngoma-like phenomena, from their reproduction mechanisms as affliction cults to their underlying logics and world visions. Apesar de ser frequentemente assumido que os sistemas de interpreta o do azar s o determinísticos, pensamos que a no o de "caos determinístico" será mais adequada para compreender os princípios subjacentes ao sistema mo ambicano de adivinha o através do tinhlolo. Este sistema assenta numa estrutura determinística, procura explicar e regular a incerteza, mas o seu resultado é caótico dada a complexidade dos factores envolvidos, desconhecidos na sua totalidade e caracterizados pela sua agência. Compreender o tinhlolo como um sistema de "domestica o do aleatório" legitima e amplifica o campo de compara o com outros contextos a nível mundial (incluindo a no o probabilística do "risco") e ressitua o estudo dos fenómenos do tipo Ngoma, dos seus mecanismos de reprodu o enquanto cultos de afli o para as suas lógicas subjacentes e vis es do mundo.

Abstract:
This paper presents an investigation of the deterministic andstochastic chaos. The modified Colpitts oscillator is used as anexample of deterministic chaos in electronic circuits. The graphicalmethod of Lorenz maps is used for graphical observation of both chaoticclasses.

Abstract:
The scope of this teaching package is to make a brief introduction to some notions and properties of chaotic systems. We first make a brief introduction to chaos in general and then we show some important properties of chaotic systems using the logistic map and its bifurcation diagram. We also show the universality found in "the route to chaos". The user is only required to have notions of algebra, so it is quite accessible. The formal basis of chaos theory are not covered in this introduction, but are pointed out for the reader interested in them. Therefore, this package is also useful for people who are interested in going deep into the mathematical theories, because it is a simple introduction of the terminology, and because it points out which are the original sources of information (so there is no danger in falling in the trap of "Learn Chaos in 48 hours" or "Bifurcation Diagrams for Dummies"). The included exercises are suggested for consolidating the covered topics. The on-line resources are highly recommended for extending this brief induction.

Abstract:
Recently, we introduced a new test for distinguishing regular from chaotic dynamics in deterministic dynamical systems and argued that the test had certain advantages over the traditional test for chaos using the maximal Lyapunov exponent. In this paper, we investigate the capability of the test to cope with moderate amounts of noisy data. Comparisons are made between an improved version of our test and both the ``tangent space'' and ``direct method'' for computing the maximal Lyapunov exponent. The evidence of numerical experiments, ranging from the logistic map to an eight-dimensional Lorenz system of differential equations (the Lorenz 96 system), suggests that our method is superior to tangent space methods and that it compares very favourably with direct methods.