Data based identification and prediction of nonlinear and complex dynamical systems

We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin

Synchrony and bifurcations in coupled dynamical systems and effects of time delay

Dynamik auf Netzwerken ist ein mathematisches Feld, das in den letzten Jahrzehnten schnell gewachsen ist und Anwendungen in zahlreichen Disziplinen wie z.B. Physik, Biologie und Soziologie findet. Die Funktion vieler Netzwerke hängt von der Fähigkeit ab, die Elemente des Netzwerkes zu synchronisieren. Mit anderen Worten, die Existenz und die transversale Stabilität der synchronen Mannigfaltigkeit sind zentrale Eigenschaften. Erst seit einigen Jahren wird versucht, den verwickelten Zusammenhang zwischen der Kopplungsstruktur und den Stabilitätseigenschaften synchroner Zustände zu verstehen. Genau das ist das zentrale Thema dieser Arbeit. Zunächst präsentiere ich erste Ergebnisse zur Klassifizierung der Kanten eines gerichteten Netzwerks bezüglich ihrer Bedeutung für die Stabilität des synchronen Zustands. Folgend untersuche ich ein komplexes Verzweigungsszenario in einem gerichteten Ring von Stuart-Landau Oszillatoren und zeige, dass das Szenario persistent ist, wenn dem Netzwerk eine schwach gewichtete Kante hinzugefügt wird. Daraufhin untersuche ich synchrone Zustände in Ringen von Phasenoszillatoren die mit Zeitverzögerung gekoppelt sind. Ich bespreche die Koexistenz synchroner Lösungen und analysiere deren Stabilität und Verzweigungen. Weiter zeige ich, dass eine Zeitverschiebung genutzt werden kann, um Muster im Ring zu speichern und wiederzuerkennen. Diese Zeitverschiebung untersuche ich daraufhin für beliebige Kopplungsstrukturen. Ich zeige, dass invariante Mannigfaltigkeiten des Flusses sowie ihre Stabilität unter der Zeitverschiebung erhalten bleiben. Darüber hinaus bestimme ich die minimale Anzahl von Zeitverzögerungen, die gebraucht werden, um das System äquivalent zu beschreiben. Schließlich untersuche ich das auffällige Phänomen eines nichtstetigen Übergangs zu Synchronizität in Klassen großer Zufallsnetzwerke indem ich einen kürzlich eingeführten Zugang zur Beschreibung großer Zufallsnetzwerke auf den Fall zeitverzögerter Kopplungen verallgemeinere.Since a couple of decades, dynamics on networks is a rapidly growing branch of mathematics with applications in various disciplines such as physics, biology or sociology. The functioning of many networks heavily relies on the ability to synchronize the network’s nodes. More precisely, the existence and the transverse stability of the synchronous manifold are essential properties. It was only in the last few years that people tried to understand the entangled relation between the coupling structure of a network, given by a (di-)graph, and the stability properties of synchronous states. This is the central theme of this dissertation. I first present results towards a classification of the links in a directed, diffusive network according to their impact on the stability of synchronization. Then I investigate a complex bifurcation scenario observed in a directed ring of Stuart-Landau oscillators. I show that under the addition of a single weak link, this scenario is persistent. Subsequently, I investigate synchronous patterns in a directed ring of phase oscillators coupled with time delay. I discuss the coexistence of multiple of synchronous solutions and investigate their stability and bifurcations. I apply these results by showing that a certain time-shift transformation can be used in order to employ the ring as a pattern recognition device. Next, I investigate the same time-shift transformation for arbitrary coupling structures in a very general setting. I show that invariant manifolds of the flow together with their stability properties are conserved under the time-shift transformation. Furthermore, I determine the minimal number of delays needed to equivalently describe the system’s dynamics. Finally, I investigate a peculiar phenomenon of non-continuous transition to synchrony observed in certain classes of large random networks, generalizing a recently introduced approach for the description of large random networks to the case of delayed couplings

Complex Systems: Nonlinearity and Structural Complexity in spatially extended and discrete systems

Resumen Esta Tesis doctoral aborda el estudio de sistemas de muchos elementos (sistemas discretos) interactuantes. La fenomenología presente en estos sistemas esta dada por la presencia de dos ingredientes fundamentales: (i) Complejidad dinámica: Las ecuaciones del movimiento que rigen la evolución de los constituyentes son no lineales de manera que raramente podremos encontrar soluciones analíticas. En el espacio de fases de estos sistemas pueden coexistir diferentes tipos de trayectorias dinámicas (multiestabilidad) y su topología puede variar enormemente dependiendo de dos parámetros usados en las ecuaciones. La conjunción de dinámica no lineal y sistemas de muchos grados de libertad (como los que aquí se estudian) da lugar a propiedades emergentes como la existencia de soluciones localizadas en el espacio, sincronización, caos espacio-temporal, formación de patrones, etc... (ii) Complejidad estructural: Se refiere a la existencia de un alto grado de aleatoriedad en el patrón de las interacciones entre los componentes. En la mayoría de los sistemas estudiados esta aleatoriedad se presenta de forma que la descripción de la influencia del entorno sobre un único elemento del sistema no puede describirse mediante una aproximación de campo medio. El estudio de estos dos ingredientes en sistemas extendidos se realizará de forma separada (Partes I y II de esta Tesis) y conjunta (Parte III). Si bien en los dos primeros casos la fenomenología introducida por cada fuente de complejidad viene siendo objeto de amplios estudios independientes a lo largo de los últimos años, la conjunción de ambas da lugar a un campo abierto y enormemente prometedor, donde la interdisciplinariedad concerniente a los campos de aplicación implica un amplio esfuerzo de diversas comunidades científicas. En particular, este es el caso del estudio de la dinámica en sistemas biológicos cuyo análisis es difícil de abordar con técnicas exclusivas de la Bioquímica, la Física Estadística o la Física Matemática. En definitiva, el objetivo marcado en esta Tesis es estudiar por separado dos fuentes de complejidad inherentes a muchos sistemas de interés para, finalmente, estar en disposición de atacar con nuevas perspectivas problemas relevantes para la Física de procesos celulares, la Neurociencia, Dinámica Evolutiva, etc..

Applying the Free-Energy Principle to Complex Adaptive Systems

The free energy principle is a mathematical theory of the behaviour of self-organising systems that originally gained prominence as a unified model of the brain. Since then, the theory has been applied to a plethora of biological phenomena, extending from single-celled and multicellular organisms through to niche construction and human culture, and even the emergence of life itself. The free energy principle tells us that perception and action operate synergistically to minimize an organism’s exposure to surprising biological states, which are more likely to lead to decay. A key corollary of this hypothesis is active inference—the idea that all behavior involves the selective sampling of sensory data so that we experience what we expect to (in order to avoid surprises). Simply put, we act upon the world to fulfill our expectations. It is now widely recognized that the implications of the free energy principle for our understanding of the human mind and behavior are far-reaching and profound. To date, however, its capacity to extend beyond our brain—to more generally explain living and other complex adaptive systems—has only just begun to be explored. The aim of this collection is to showcase the breadth of the free energy principle as a unified theory of complex adaptive systems—conscious, social, living, or not

Mathematical modeling, simulation and analysis of metabolic oscillations in Bacillus subtilis biofilms

Metabolic oscillations in biofilms of Bacillus subtilis have been reported as periodic halting of growth in the expansion of the colony growing in a microfluidics chamber by Liu et al (2015). This thesis is aimed at understanding these oscillations through minimal dynamic model involving three ordinary differential equations (ODEs). The model is first applied in its basic form in order to describe the oscillations. Next, various modifications of the model are discussed in detail and the results of each modification are viewed in light of the underlying biology. The four modifications investigate the mechanism of oscillations with respect to spatial effects, reversible reactions and more robust reaction kinetics. Finally, we apply the minimal model in a broader perspective in order to understand population dynamics in a typical community of a social organism. We consider three interacting subpopulations of a species that have their own distinct phenotypes. None of the subpopulations have an absolute advantage over the other two. This gives rise to cyclic dynamics like the rock paper scissors game which is analysed using evolutionary game theory. We also present an asymmetrical two-player two- strategy game describing the same system, where the phenotype of each subpopulation is considered as a strategy. This investigation tests the ideal strategies for three different levels of antibiotic stress. We observe bet-hedging in the form of production of resistant cells which are a costly choice in the absence of the antibiotic stress. Although the population dynamics study is described with a broad range of applicability, we also discuss its applications in the B. subtilis biofilm

Modeling and Optimal Operation of Hydraulic, Wind and Photovoltaic Power Generation Systems

The transition to 100% renewable energy in the future is one of the most important ways of achieving "carbon peaking and carbon neutrality" and of reducing the adverse effects of climate change. In this process, the safe, stable and economical operation of renewable energy generation systems, represented by hydro-, wind and solar power, is particularly important, and has naturally become a key concern for researchers and engineers. Therefore, this book focuses on the fundamental and applied research on the modeling, control, monitoring and diagnosis of renewable energy generation systems, especially hydropower energy systems, and aims to provide some theoretical reference for researchers, power generation departments or government agencies

Aeronautical engineering: A continuing bibliography with indexes (supplement 304)

This bibliography lists 453 reports, articles, and other documents introduced into the NASA scientific and technical information system in May 1994. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment, and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics

Modelling, Monitoring, Control and Optimization for Complex Industrial Processes

This reprint includes 22 research papers and an editorial, collected from the Special Issue "Modelling, Monitoring, Control and Optimization for Complex Industrial Processes", highlighting recent research advances and emerging research directions in complex industrial processes. This reprint aims to promote the research field and benefit the readers from both academic communities and industrial sectors

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