Nonlinear Climate Dynamics
Nonlinear Climate Dynamics

Author: Henk A. Dijkstra

Publisher: Cambridge University Press

Published: 2013-06-17

Total Pages: 371

ISBN-13: 1107244374

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This book introduces stochastic dynamical systems theory in order to synthesize our current knowledge of climate variability. Nonlinear processes, such as advection, radiation and turbulent mixing, play a central role in climate variability. These processes can give rise to transition phenomena, associated with tipping or bifurcation points, once external conditions are changed. The theory of dynamical systems provides a systematic way to study these transition phenomena. Its stochastic extension also forms the basis of modern (nonlinear) data analysis techniques, predictability studies and data assimilation methods. Early chapters apply the stochastic dynamical systems framework to a hierarchy of climate models to synthesize current knowledge of climate variability. Later chapters analyse phenomena such as the North Atlantic Oscillation, El Niño/Southern Oscillation, Atlantic Multidecadal Variability, Dansgaard–Oeschger events, Pleistocene ice ages and climate predictability. This book will prove invaluable for graduate students and researchers in climate dynamics, physical oceanography, meteorology and paleoclimatology.

Nonlinear and Stochastic Climate Dynamics
Nonlinear and Stochastic Climate Dynamics

Author: Christian L. E. Franzke

Publisher: Cambridge University Press

Published: 2017-01-19

Total Pages: 612

ISBN-13: 1316883213

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It is now widely recognized that the climate system is governed by nonlinear, multi-scale processes, whereby memory effects and stochastic forcing by fast processes, such as weather and convective systems, can induce regime behavior. Motivated by present difficulties in understanding the climate system and to aid the improvement of numerical weather and climate models, this book gathers contributions from mathematics, physics and climate science to highlight the latest developments and current research questions in nonlinear and stochastic climate dynamics. Leading researchers discuss some of the most challenging and exciting areas of research in the mathematical geosciences, such as the theory of tipping points and of extreme events including spatial extremes, climate networks, data assimilation and dynamical systems. This book provides graduate students and researchers with a broad overview of the physical climate system and introduces powerful data analysis and modeling methods for climate scientists and applied mathematicians.

Nonlinear Dynamics
Nonlinear Dynamics

Author: George Datseris

Publisher: Springer Nature

Published: 2022-03-13

Total Pages: 243

ISBN-13: 3030910326

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This concise and up-to-date textbook provides an accessible introduction to the core concepts of nonlinear dynamics as well as its existing and potential applications. The book is aimed at students and researchers in all the diverse fields in which nonlinear phenomena are important. Since most tasks in nonlinear dynamics cannot be treated analytically, skills in using numerical simulations are crucial for analyzing these phenomena. The text therefore addresses in detail appropriate computational methods as well as identifying the pitfalls of numerical simulations. It includes numerous executable code snippets referring to open source Julia software packages. Each chapter includes a selection of exercises with which students can test and deepen their skills.

Nonlinear Climate Dynamics
Nonlinear Climate Dynamics

Author: Henk A. Dijkstra

Publisher: Cambridge University Press

Published: 2013-06-17

Total Pages: 371

ISBN-13: 0521879175

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This book presents stochastic dynamical systems theory in order to synthesize our current knowledge of climate variability, for graduate students and researchers.

Nonlinear Dynamics and Chaos: Advances and Perspectives
Nonlinear Dynamics and Chaos: Advances and Perspectives

Author: Marco Thiel

Publisher: Springer

Published: 2010-05-17

Total Pages: 300

ISBN-13: 3642046290

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This book is a collection of papers contributed by some of the greatest names in the areas of chaos and nonlinear dynamics. Each paper examines a research topic at the frontier of the area of dynamical systems. As well as reviewing recent results, each paper also discusses the future perspectives of each topic. The result is an invaluable snapshot of the state of the ?eld by some of the most important researchers in the area. The ?rst contribution in this book (the section entitled “How did you get into Chaos?”) is actually not a paper, but a collection of personal accounts by a number of participants of the conference held in Aberdeen in September 2007 to honour Celso Grebogi’s 60th birthday. At the instigation of James Yorke, many of the most well-known scientists in the area agreed to share their tales on how they got involved in chaos during a celebratory dinner in Celso’s honour during the conference. This was recorded in video, we felt that these accounts were a valuable historic document for the ?eld. So we decided to transcribe it and include it here as the ?rst section of the book.

Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos

Author: Steven H. Strogatz

Publisher: CRC Press

Published: 2018-05-04

Total Pages: 532

ISBN-13: 0429961111

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This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

Nonlinear Physical Oceanography
Nonlinear Physical Oceanography

Author: Henk A. Dijkstra

Publisher: Springer Science & Business Media

Published: 2007-07-16

Total Pages: 532

ISBN-13: 1402022638

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Taken from a review of the first edition in SIAM: "This text is different from most others in that it combines several different disciplines and draws on many scientific studies in order to deduce mechanisms of ocean circulation. (...) Therefore (it) cannot be substituted, and (...) it meets its unique goals with clarity and thoroughness".

Nonlinear Dynamics
Nonlinear Dynamics

Author: Marc R Roussel

Publisher: Morgan & Claypool Publishers

Published: 2019-05-01

Total Pages: 190

ISBN-13: 1643274643

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This book uses a hands-on approach to nonlinear dynamics using commonly available software, including the free dynamical systems software Xppaut, Matlab (or its free cousin, Octave) and the Maple symbolic algebra system. Detailed instructions for various common procedures, including bifurcation analysis using the version of AUTO embedded in Xppaut, are provided. This book also provides a survey that can be taught in a single academic term covering a greater variety of dynamical systems (discrete versus continuous time, finite versus infinite-dimensional, dissipative versus conservative) than is normally seen in introductory texts. Numerical computation and linear stability analysis are used as unifying themes throughout the book. Despite the emphasis on computer calculations, theory is not neglected, and fundamental concepts from the field of nonlinear dynamics such as solution maps and invariant manifolds are presented.

Nonlinear Dynamics in Physiology
Nonlinear Dynamics in Physiology

Author: Mark Shelhamer

Publisher: World Scientific

Published: 2007

Total Pages: 367

ISBN-13: 9812700293

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This book provides a compilation of mathematical-computational tools that are used to analyze experimental data. The techniques presented are those that have been most widely and successfully applied to the analysis of physiological systems, and address issues such as randomness, determinism, dimension, and nonlinearity. In addition to bringing together the most useful methods, sufficient mathematical background is provided to enable non-specialists to understand and apply the computational techniques. Thus, the material will be useful to life-science investigators on several levels, from physiologists to bioengineer.Initial chapters present background material on dynamic systems, statistics, and linear system analysis. Each computational technique is demonstrated with examples drawn from physiology, and several chapters present case studies from oculomotor control, neuroscience, cardiology, psychology, and epidemiology. Throughout the text, historical notes give a sense of the development of the field and provide a perspective on how the techniques were developed and where they might lead. The overall approach is based largely on the analysis of trajectories in the state space, with emphasis on time-delay reconstruction of state-space trajectories. The goal of the book is to enable readers to apply these methods to their own research.

Applied Nonlinear Dynamics
Applied Nonlinear Dynamics

Author: Ali H. Nayfeh

Publisher: John Wiley & Sons

Published: 2008-11-20

Total Pages: 700

ISBN-13: 3527617558

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A unified and coherent treatment of analytical, computational and experimental techniques of nonlinear dynamics with numerous illustrative applications. Features a discourse on geometric concepts such as Poincaré maps. Discusses chaos, stability and bifurcation analysis for systems of differential and algebraic equations. Includes scores of examples to facilitate understanding.