A simple asset pricing model with two types of adaptively learning traders, fundamentalists and technical analysts, is studied. Fractions of these trader types, which are both boundedly rational, change over time according to evolutionary learning, with technical analysts conditioning their forecasting rule upon deviations from a benchmark fundamental. Volatility clustering arises endogenously in this model. Two mechanisms are proposed as an explanation. The first is coexistence of a stable steady state and a stable limit cycle, which arise as a consequence of a so-called Chenciner bifurcation of the system. The second is intermittency and associated bifurcation routes to strange attractors. Both phenomena are persistent and occur generically in nonlinear multi-agent evolutionary systems. (author's abstract) / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

I present a simple model of an evolutionary financial market with heterogeneous agents, based on the concept of adaptive belief systems introduced by Brock and Hommes (1997a). Agents choose between different forecast rules based on past performance, resulting in an evolutionary dynamics across predictor choice coupled to the equilibrium dynamics. The model generates endogenous price fluctuations with similar statistical properties as those observed in real return data, such as fat tails and volatility clustering. These similarities are demonstrated for data from the British, German, and Austrian stock market. (author's abstract) / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

Systems whose time evolutions are entirely deterministic can nevertheless be studied probabilistically, <em>i. e. </em> in terms of the evolution of probability distributions rather than individual trajectories. This approach is central to the dynamics of ensembles (statistical mechanics) and systems with uncertainty in the initial conditions. It is also the basis of ergodic theory--the study of probabilistic invariants of dynamical systems--which provides one framework for understanding chaotic systems whose time evolutions are erratic and for practical purposes unpredictable. Delay differential equations (DDEs) are a particular class of deterministic systems, distinguished by an explicit dependence of the dynamics on past states. DDEs arise in diverse applications including mathematics, biology and economics. A probabilistic approach to DDEs is lacking. The main problems we consider in developing such an approach are (1) to characterize the evolution of probability distributions for DDEs, <em>i. e. </em> develop an analog of the Perron-Frobenius operator; (2) to characterize invariant probability distributions for DDEs; and (3) to develop a framework for the application of ergodic theory to delay equations, with a view to a probabilistic understanding of DDEs whose time evolutions are chaotic. We develop a variety of approaches to each of these problems, employing both analytical and numerical methods. In transient chaos, a system evolves erratically during a transient period that is followed by asymptotically regular behavior. Transient chaos in delay equations has not been reported or investigated before. We find numerical evidence of transient chaos (fractal basins of attraction and long chaotic transients) in some DDEs, including the Mackey-Glass equation. Transient chaos in DDEs can be analyzed numerically using a modification of the "stagger-and-step" algorithm applied to a discretized version of the DDE.

Epilepsy is a serious neurological disorder characterized by recurrent unprovoked seizures due to abnormal or excessive neuronal activity in the brain. An estimated 50 million people around the world suffer from this condition, and it is classified as the second most serious neurological disease known to humanity, after stroke. With early and accurate detection of seizures, doctors can gain valuable time to administer medications and other such anti-seizure countermeasures to help reduce the damaging effects of this crippling disorder. The time-varying dynamics and high inter-individual variability make early prediction of a seizure state a challenging task. Many studies have shown that EEG signals do have valuable information that, if correctly analyzed, could help in the prediction of seizures in epileptic patients before their occurrence. Several mathematical transforms have been analyzed for its correlation with seizure onset prediction and a series of experiments were done to certify their strengths. New algorithms are presented to help clarify, monitor, and cross-validate the classification of EEG signals to predict the ictal (i.e. seizure) states, specifically the preictal, interictal, and postictal states in the brain. These new methods show promising results in detecting the presence of a preictal phase prior to the ictal state.

An analog controller has been analyzed and built for an electrostatic micro-cantilever beam. The closed loop MEMS device can be used as both actuator and sensor. As an actuator it will have the advantage of large stable travel range up to 90% of the gap. As a sensor the beam is to be driven into chaotic motion which is very sensitive changes in the system parameters. Two versions of the controller have been analyzed and implemented, one for the actuator and one for the sensor. For the actuator, preliminary experiments show good matching with the model. As for the sensor, the dynamic behavior have been studied and the best operating regions have been determined.

The aim of this essay is to discuss the meaning of the human and its possible overcoming in Friedrich Nietzsche’s doctrine of the eternal recurrence of the same, with Martin Heidegger’s readings of Nietzsche as point of departure. According to Heidegger, Nietzsche’s doctrine of the eternal recurrence of the same represents the end of occidental metaphysical thinking. The thought concludes a thinking of being as the presence of beings, where the original question of being was never developed out of its own ground. But at the heart of this interpretation, often considered “violent”, lies the question of whether man is able to think being out of his finitude. This is the question I will unfold, through a reading of Nietzsche’s thought of the eternal recurrence of the same, as it is presented in his Thus spoke Zarathustra, as an attempt to think beings in their being beyond a “humanization” of them, expressed in transcendental aims, purposes and categories. This attempt, I argue, is essentially bound up with a comportment toward the human self as the finite and the corporal. In this sense the human being in its finitude and corporeality is thefocus and the basis for the search for “the overman”. But this focus on man, as he who can overcome himself, is at the same time a focus that canbe said to lead man away from himself, in not asking the deeper question about what it means to be this human being. I will furthermore consider the tragic as the theme where this question of the overcoming of the human comes to the fore; the dionysic-tragic reveals both a view of man as the being that is mastered by the abyss that underlies this world, and therefore mastered by his finitude - and as the being who can master this same abyss, in thinking it as one with the human self. The purpose is not to take a position for or against Heidegger’s reading, but to develop a discussion between Heidegger and Nietzsche about the human self as always being both the closed and the open, and about the ways in which human thinking can approach this.

The thesis develops two characterizations of spatio-temporal complex patterns. While these are developed for the patterns of fluid flow in experiments on Rayleigh-Benard Convection(RBC), they are adaptable to a wide range of spatially extended systems. The characterizations may be especially useful in cases where one does not have good models describing the dynamics, making numerical and analytic studies difficult. In Spiral Defect Chaos(SDC), a weakly turbulent regime of RBC, the convective rolls exhibit complex spatial and temporal dynamics. We study the dynamics of SDC through local defect formations between convective rolls as well as the topological rearrangements of these rolls at a global scale. A laser based thermal actuation system is developed to reproducibly impose initial states for the fluid flow and construct ensembles of trajectories in the neighborhood of defect nucleation. This is used to extract the modes and their growth rates, characterizing the linear manifold corresponding to defect nucleation. The linear manifold corresponding to instabilities resulting in defect formation is key to building efficient schemes to control the dynamics exhibited. We also develop the use of computational homology as a tool to study spatially extended dynamical systems. A quantitative measure of the topological features of patterns is shown to provide insights into the underlying dynamics not easily uncovered otherwise. In the case of RBC, the homology of the patterns is seen to indicate asymmetries between hot and cold regions of the flow, stochastic evolution at a global scale as well as bifurcations occurring well into the turbulent regime of the flow.

Chaotic dynamics are at the center of multiple studies to perfect encrypted communication systems. Indeed, the particular time evolution nature of chaotic signals constitutes the fundamentals of their application to secure telecommunications. The pseudo random signal constitutes the carrier wave for the communication. The information coded on the carrier wave can be extracted with knowledge of the system dynamic evolution law. This evolution law consists of a second-order delay differential equation in which intervene the various parameters of the physical system setup. The set of precise parameter values forms the key, in a cryptographic sense, of the encrypted transmission. This thesis work presents the implementation of an experimental encryption system using chaos. The optical intensity of the emitter fluctuates chaotically and serves as carrier wave. A message of small amplitude, hidden inside the fluctuations of the carrier wave, is extracted from the transmitted signal by a properly tuned receiver. The influence of the message modulation format on the communication quality both in the back to back case and after propagation is investigated numerically.

OOPS stands for Opensource Opencourseware Prototype System, a project sponsored by Fantasy Foundation. Aiming to benefit Chinese readers, this project recruit volunteer translators all over the world through internet to translate Opencourseware materials from Massachusetts Institute of Technology (MIT) into Chinese. This research was a qualitative case study conducted between 2004/2 ~ 2007/1. Multiple data sources were surveyed, including OOPS¡¦ online discussion forum, and archival information from OOPS website. Online archival data ranged from media reports, activity reports, e-newsletters, volunteer reports, survey summaries, and sub-group websites. Interviews with group leaders were also conducted. Evidence collected through these means were used to describe how OOPS employed the Internet to coordinate translation efforts and promote Opencourseware. In addition, this research applied Science of Complexity to explain the self organizing phenomenon within the network arisen from its participants. This research looked further into how Science of Complexity can clarify the organic process of a self organizing network going from simple to complex. This research found 1) the degree of openness in a collaborative knowledge network influenced its degree of self organization; 2) volunteer¡¦s willingness to participate was related to environment¡¦s fitness; 3) critical mass, diversity, variety, interaction and feedback promoted evolution; 4) a collaborative knowledge network¡¦s key to an organic expansion depended on participants¡¦ outgrowth and self organization; and 5) effective facilitation at the edge of chaos would foster new organization growth.

Population dynamics is the dominant branch of mathematical biology. The first model for population dynamics was developed by Thomas Malthus. A more complicated model was developed by Pierre Fran&ccedil / ois Verhulst and it is called the logistic equation. Our aim in this thesis is to extend the models using piecewise constant arguments and to find the conditions when the models have fixed points, periodic solutions and chaos with investigation of stability of periodic solutions.