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Many nonlinear systems around us can generate a very complex and counter-intuitive dynamics that contrasts with their simplicity, but their understanding requires concepts that are outside the basic training of most science students. This textbook, which is the fruit of graduate courses that the authors have taught at their respective universities, provides a richly illustrated introduction to nonlinear dynamical systems and chaos and a solid foundation for this fascinating subject. It will satisfy those who want discover this field, including at the undergraduate level, but also those who need a compact and consistent overview, gathering the concepts essential to nonlinear scientists.The first and second chapters describe the essential concepts needed to describe nonlinear dynamical systems as well as their stability. The third chapter introduces the concept of bifurcation, where the qualitative dynamical behavior of a system changes. The fourth chapter deals with oscillations, from their birth to their destabilization, and how they respond to external driving. The fifth and sixth chapters discuss complex behaviors that only occur in state spaces of dimension three and higher: quasi-periodicity and chaos, from their general properties to quantitative methods of characterization. All chapters are supplemented by exercises ranging from direct applications of the notions introduced in the corresponding chapter to elaborate problems involving concepts from different chapters, as well as numerical explorations.

Dynamics. --- Bifurcation. --- Chaos Theory. --- Dynamic System. --- Nonlinear Dynamics. --- Strange Attractor.

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In its second expanded and updated edition, this textbook covers the theory and applications of dynamical processes whose time evolution is not continuous, but rather is modeled in discrete time steps through difference equations. These discrete models play an increasingly important role - reinforced by the use of computers - in science, engineering and economics. This new edition also covers special applications in financial mathematics. Following a basic introduction with examples, the first part provides a thorough survey of linear systems and their stability properties.The second part deals with nonlinear systems, especially their stability, and includes an excursus on chaos and fractals and an introduction into the more recent theory of positive dynamical systems along with applications in biology and economics. In seiner zweiten erweiterten und aktualisierten Auflage befasst sich dieses Lehrbuch mit der Theorie und den Anwendungen von dynamischen Prozessen, deren zeitliche Entwicklung nicht kontinuierlich, sondern in diskreten Zeitschritten durch Differenzengleichungen modelliert wird. Verstärkt noch durch den Einsatz von Computern spielen die diskreten Modelle eine zunehmend wichtige Rolle in den Natur-, Ingenieur- und Wirtschaftswissenschaften. Daher werden in dieser Neuauflage zusätzlich auch Anwendungen in der Finanzmathematik betrachtet. Nach einer grundlegenden Einführung mit Beispielen werden im ersten Teil lineare Systeme und ihre Stabilitätseigenschaften gründlich behandelt. Der zweite Teil befasst sich mit nichtlinearen Systemen, insbesondere deren Stabilität, und enthält einen Exkurs zu Chaos und Fraktalen sowie eine Einführung in die neuere Theorie positiver dynamischer Systeme nebst Anwendungen in Biologie und Ökonomie.

Difference equations. --- Dynamics --- Data processing. --- Difference Equation. --- Discreet System. --- Dynamic System. --- Financial Mathematics.

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This volume sheds empirical light on Complex Dynamic Systems Theory (CDST) by providing five sets of analyses of two longitudinal, interactional datasets, involving two dyads exchanging emails over one academic semester. The collective study on CDST is the first of its kind, in that it delves into multiple subsystems of learner language, traversing the domains of morphosyntax, semantics, pragmatics and discourse. The data analyses expose the dynamics of the interactional process, offering evidence of core characteristics of complex dynamic systems: sensitive dependence on initial conditions, interconnectedness of subsystems, the emergence of attractor states over time and variation in and between the individuals. Together, the analyses, each alone an engaging description, capture fine-grained patterns of change over time. More importantly, they demonstrate the impact of the ecosystem on individuals’ use of language. The book offers critical insights relevant to CDST researchers, theorists and empiricists alike, as well as to teachers seeking a nuanced understanding of the learning benefits of computer-mediated interactional activities.

Second language acquisition --- Language and languages --- System theory. --- Systems, Theory of --- Systems science --- Science --- Foreign language study --- Language and education --- Language schools --- Second language learning --- Language acquisition --- Study and teaching. --- Philosophy --- System theory --- #KVHA:Taalkunde --- #KVHA:Taalonderwijs --- #KVHA:Tweede taalonderwijs --- Study and teaching --- Asynchronous interaction. --- CDST. --- Complex Dynamic System Theory. --- Complexity system. --- Computer-mediated dyadic interaction. --- Dynamic system. --- Interlanguage. --- Learner language. --- SLA. --- morphosyntax. --- pragmatics. --- research methodology. --- semantics. --- Language and languages Study and teaching --- Second language acquisition Study and teaching

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This book appeals to scientists, teachers and graduate students in mathematics, and will be of interest for scholars in applied sciences as well, in particular in medicine, biology and social sciences. The models in this connection apply, in particular, to the study of the immune system response and to the predator–prey dynamic. The efficiency of public transport is also considered and blast waves in explosions are studied. Other contributions concern pure mathematics, in particular Pythagorean means, sequences of matrices and Markov chains, and these give evidence of deep links with Symmetry.

Research & information: general --- Mathematics & science --- paradox of enrichment --- prey–predator system --- persistence of predators --- extinction of predators --- blast waves --- non-ideal gas --- Rankine–Hugoniot conditions --- magnetogasdynamics --- dynamic model --- immune system response --- immune cells --- abnormal cells --- nonlinear ordinary differential equations --- stability --- diet --- Aggregation dynamic system --- Discrete system --- Epidemic model --- Cauchy’s interlacing theorem --- Output-feedback control --- Stability --- Antistable/Stable matrix --- onboard comfort level --- Markow chain --- bus passenger occupancy prediction --- Chebyshev inequality --- Tracy-Singh product --- continuous field of operators --- Bochner integral --- weighted Pythagorean mean

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This book comprises ten articles covering different aspects of power quality issues in microgrids and distributed generation (DG) systems, including 1) Detection and estimation of power quality; 2) Modeling; 3) Harmonic control for DG systems and microgrids; 4) Stability improvements for microgrids. Different power quality phenomena and solution were studied in the included papers, such as harmonics, resonance, frequency deviation, voltage sag, and fluctuation. From a network point of view, some papers studied the harmonic and stability issues in standalone microgrids which are more likely to cause power quality problems. Other papers discussed the power quality problems in microgrids which are weakly interconnected with the main distribution grid. In view of the published papers, there is a trend that increasingly advanced modeling, analysis, and control schemes were applied in the studies. Moreover, the latest works focus not only on single-unit problems but also multiple units or network issues. Although some of the hot topics are not included, this book covers multiple aspects of the current power quality research frontier, and represents a particularly useful reference book for frontier researchers in this field.

power quality improvement --- differential feedforward --- weak grid --- data testing --- distributed generations --- voltage-source converter --- dynamic frequency support --- coordinated control --- grid-connection/island switching process --- virtual damping --- PV generation --- virtual inertia --- autonomous microgrid --- optimal virtual resistor --- multi-inverter system --- standalone microgrid --- unscented Kalman filter --- HVDC --- voltage fluctuation --- solar photovoltaic system --- nonlinear dynamic system --- state estimation --- voltage stability --- diesel generator --- voltage control --- multi-time scale --- sliding mode control --- power system simulation --- stability analysis --- grid impedance --- modeling method --- shunt inverter --- voltage compensation --- 2nd-order lowpass filter --- virtual synchronous generator --- microgrid --- output impedance --- hybrid energy storage --- grid-connected inverter --- parameter identification --- wind farm --- frequency stability --- harmonic suppression --- current source mode (CSM) --- voltage source mode (VSM) --- stand-alone microgrid --- frequency control --- vector control --- power quality control --- grid-tied inverter --- submarine cables --- line commutated converter --- reference current compensation --- power quality --- series inverter --- impedance enhancement