Physics and Applications of Laser Diode Chaos

An overview of chaos in laser diodes is provided which surveys experimental achievements in the area and explains the theory behind the phenomenon. The fundamental physics underpinning this behaviour and also the opportunities for harnessing laser diode chaos for potential applications are discussed. The availability and ease of operation of laser diodes, in a wide range of configurations, make them a convenient test-bed for exploring basic aspects of nonlinear and chaotic dynamics. It also makes them attractive for practical tasks, such as chaos-based secure communications and random number generation. Avenues for future research and development of chaotic laser diodes are also identified.Comment: Published in Nature Photonic

Optimal self-induced stochastic resonance in multiplex neural networks: electrical versus chemical synapses

Electrical and chemical synapses shape the dynamics of neural networks and their functional roles in information processing have been a longstanding question in neurobiology. In this paper, we investigate the role of synapses on the optimization of the phenomenon of self-induced stochastic resonance in a delayed multiplex neural network by using analytical and numerical methods. We consider a two-layer multiplex network, in which at the intra-layer level neurons are coupled either by electrical synapses or by inhibitory chemical synapses. For each isolated layer, computations indicate that weaker electrical and chemical synaptic couplings are better optimizers of self-induced stochastic resonance. In addition, regardless of the synaptic strengths, shorter electrical synaptic delays are found to be better optimizers of the phenomenon than shorter chemical synaptic delays, while longer chemical synaptic delays are better optimizers than longer electrical synaptic delays -- in both cases, the poorer optimizers are in fact worst. It is found that electrical, inhibitory, or excitatory chemical multiplexing of the two layers having only electrical synapses at the intra-layer levels can each optimize the phenomenon. And only excitatory chemical multiplexing of the two layers having only inhibitory chemical synapses at the intra-layer levels can optimize the phenomenon. These results may guide experiments aimed at establishing or confirming the mechanism of self-induced stochastic resonance in networks of artificial neural circuits, as well as in real biological neural networks.Comment: 24 pages, 7 figure

Physics-based Machine Learning Approaches to Complex Systems and Climate Analysis

Komplexe Systeme wie das Klima der Erde bestehen aus vielen Komponenten, die durch eine komplizierte Kopplungsstruktur miteinander verbunden sind. Für die Analyse solcher Systeme erscheint es daher naheliegend, Methoden aus der Netzwerktheorie, der Theorie dynamischer Systeme und dem maschinellen Lernen zusammenzubringen. Durch die Kombination verschiedener Konzepte aus diesen Bereichen werden in dieser Arbeit drei neuartige Ansätze zur Untersuchung komplexer Systeme betrachtet. Im ersten Teil wird eine Methode zur Konstruktion komplexer Netzwerke vorgestellt, die in der Lage ist, Windpfade des südamerikanischen Monsunsystems zu identifizieren. Diese Analyse weist u.a. auf den Einfluss der Rossby-Wellenzüge auf das Monsunsystem hin. Dies wird weiter untersucht, indem gezeigt wird, dass der Niederschlag mit den Rossby-Wellen phasenkohärent ist. So zeigt der erste Teil dieser Arbeit, wie komplexe Netzwerke verwendet werden können, um räumlich-zeitliche Variabilitätsmuster zu identifizieren, die dann mit Methoden der nichtlinearen Dynamik weiter analysiert werden können. Die meisten komplexen Systeme weisen eine große Anzahl von möglichen asymptotischen Zuständen auf. Um solche Zustände zu beschreiben, wird im zweiten Teil die Monte Carlo Basin Bifurcation Analyse (MCBB), eine neuartige numerische Methode, vorgestellt. Angesiedelt zwischen der klassischen Analyse mit Ordnungsparametern und einer gründlicheren, detaillierteren Bifurkationsanalyse, kombiniert MCBB Zufallsstichproben mit Clustering, um die verschiedenen Zustände und ihre Einzugsgebiete zu identifizieren. Bei von Vorhersagen von komplexen Systemen ist es nicht immer einfach, wie Vorwissen in datengetriebenen Methoden integriert werden kann. Eine Möglichkeit hierzu ist die Verwendung von Neuronalen Partiellen Differentialgleichungen. Hier wird im letzten Teil der Arbeit gezeigt, wie hochdimensionale räumlich-zeitlich chaotische Systeme mit einem solchen Ansatz modelliert und vorhergesagt werden können.Complex systems such as the Earth's climate are comprised of many constituents that are interlinked through an intricate coupling structure. For the analysis of such systems it therefore seems natural to bring together methods from network theory, dynamical systems theory and machine learning. By combining different concepts from these fields three novel approaches for the study of complex systems are considered throughout this thesis. In the first part, a novel complex network construction method is introduced that is able to identify the most important wind paths of the South American Monsoon system. Aside from the importance of cross-equatorial flows, this analysis points to the impact Rossby Wave trains have both on the precipitation and low-level circulation. This connection is then further explored by showing that the precipitation is phase coherent to the Rossby Wave. As such, the first part of this thesis demonstrates how complex networks can be used to identify spatiotemporal variability patterns within large amounts of data, that are then further analysed with methods from nonlinear dynamics. Most complex systems exhibit a large number of possible asymptotic states. To investigate and track such states, Monte Carlo Basin Bifurcation analysis (MCBB), a novel numerical method is introduced in the second part. Situated between the classical analysis with macroscopic order parameters and a more thorough, detailed bifurcation analysis, MCBB combines random sampling with clustering methods to identify and characterise the different asymptotic states and their basins of attraction. Forecasts of complex system are the next logical step. When doing so, it is not always straightforward how prior knowledge in data-driven methods. One possibility to do is by using Neural Partial Differential Equations. Here, it is demonstrated how high-dimensional spatiotemporally chaotic systems can be modelled and predicted with such an approach in the last part of the thesis

Nonlinear physics of electrical wave propagation in the heart: a review

The beating of the heart is a synchronized contraction of muscle cells (myocytes) that are triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media and their application to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact in cardiac arrhythmias.Peer ReviewedPreprin

Effects of Turbulent Flows and Superdiffusion on Reaction-Dffusion Systems

The basic question underlying the work presented in this thesis concerns the self-organization and pattern formation in inanimate media when a fluid flow is present. This thesis studies the active and passive transport in turbulent and chaotic fluid flows. Thereby the focus is mainly of experimental nature. Especial interest is placed on the experimental observation and description of new patterns emerging, when active media is subjected to a turbulent fluid flow. In particular the effect of intense mixing as can be achieved by highly chaotic or turbulent fluid flows is to be uncovered. The first goal is to characterize and explain the phenomenon of a global reactive wave in a similar experimental realization observed by Fernandez Garca et al. in 2008. One step towards this goal is the measurement of the mixing caused by the Faraday experiment. This experiment consists in the vertical forcing of a container filled with liquid. Once the velocity field had been characterized we aimed for a definition of suitable analysis methods in order to study the transport of active media on different time and length-scales. Especially for intermediate range Damkoehler numbers, i.e. where the ratio of the timescale of the fluid flow and those of the reaction timescale is similar has not been studied in an experimental system with an excitable chemical reaction before. The analysis tools applied to this experimental model system might also partly be valid for the characterization of other reaction-diffusion-advection processes as found in many natural and men-made systems, such as plankton blooms in the ocean, chemicals in the atmosphere or bioreactors. The understanding of the role of the interplay of the typical timescales of the reaction and advection processes are to be discovered. A simple model accounting partly for some of the observed characteristics, such as the local scale-free transport, is formulated. The interplay of diffusive and advective processes is further studied in detail for a numerical model flow imitating the gulf-stream current. The details of this interplay can also lead to superdiffusion and scale-free transport

Synchronicity from synchronized chaos

The synchronization of loosely-coupled chaotic oscillators, a phenomenon investigated intensively for the last two decades, may realize the philosophical concept of “synchronicity”—the commonplace notion that related eventsmysteriously occur at the same time. When extended to continuous media and/or large discrete arrays, and when general (non-identical) correspondences are considered between states, intermittent synchronous relationships indeed become ubiquitous. Meaningful synchronicity follows naturally if meaningful events are identified with coherent structures, defined by internal synchronization between remote degrees of freedom; a condition that has been posited as necessary for synchronizability with an external system. The important case of synchronization between mind and matter is realized if mind is analogized to a computer model, synchronizing with a sporadically observed system, as in meteorological data assimilation. Evidence for the ubiquity of synchronization is reviewed along with recent proposals that: (1) synchronization of different models of the same objective process may be an expeditious route to improved computational modeling and may also describe the functioning of conscious brains; and (2) the nonlocality in quantum phenomena implied by Bell’s theorem may be explained in a variety of deterministic (hidden variable) interpretations if the quantum world resides on a generalized synchronization “manifold”.publishedVersio

18th IEEE Workshop on Nonlinear Dynamics of Electronic Systems: Proceedings

Proceedings of the 18th IEEE Workshop on Nonlinear Dynamics of Electronic Systems, which took place in Dresden, Germany, 26 – 28 May 2010.:Welcome Address ........................ Page I Table of Contents ........................ Page III Symposium Committees .............. Page IV Special Thanks ............................. Page V Conference program (incl. page numbers of papers) ................... Page VI Conference papers Invited talks ................................ Page 1 Regular Papers ........................... Page 14 Wednesday, May 26th, 2010 ......... Page 15 Thursday, May 27th, 2010 .......... Page 110 Friday, May 28th, 2010 ............... Page 210 Author index ............................... Page XII

A study of synchronization of nonlinear oscillators: Application to epileptic seizures

This dissertation focuses on several problems in neuroscience from the perspective of nonlinear dynamics and stochastic processes. The first part concerns a method to visualize the idea of the power spectrum of spike trains, which has an educational value to introductory students in biophysics. The next part consists of experimental and computational work on drug-induced epileptic seizures in the rat neocortex. In the experimental part, spatiotemporal patterns of electrical activities in the rat neocortex are measured using voltage-sensitive dye imaging. Epileptic regions show well-synchronized, in-phase activity during epileptic seizures. In the computational part, a network of a Hodgkin-Huxley type neocortical neural model is constructed. Phase reduction, which is a dimension reduction technique for a stable limit cycle, is applied to the system. The results propose a possible mechanism for the initiation of the drug-induced seizure as a result of a bifurcation. In the last part, a theoretical framework is developed to obtain the statistics for the period of oscillations of a stable limit cycle under stochastic perturbation. A stochastic version of phase reduction and first passage time analysis are utilized for this purpose. The method presented here shows a good agreement with numerical results for the weak noise regime --Abstract, page iii