Mathematics Of Complexity And Dynamical Systems

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Mathematics of Complexity and Dynamical Systems

Author : Robert A. Meyers
Publisher : Springer Science & Business Media
ISBN 13 : 1461418054
Total Pages : 1885 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Mathematics of Complexity and Dynamical Systems by : Robert A. Meyers

Download or read book Mathematics of Complexity and Dynamical Systems written by Robert A. Meyers and published by Springer Science & Business Media. This book was released on 2011-10-05 with total page 1885 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

Chaos and Dynamical Systems

Author : David P. Feldman
Publisher : Princeton University Press
ISBN 13 : 0691161526
Total Pages : 262 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Chaos and Dynamical Systems by : David P. Feldman

Download or read book Chaos and Dynamical Systems written by David P. Feldman and published by Princeton University Press. This book was released on 2019-08-06 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos and Dynamical Systems presents an accessible, clear introduction to dynamical systems and chaos theory, important and exciting areas that have shaped many scientific fields. While the rules governing dynamical systems are well-specified and simple, the behavior of many dynamical systems is remarkably complex. Of particular note, simple deterministic dynamical systems produce output that appears random and for which long-term prediction is impossible. Using little math beyond basic algebra, David Feldman gives readers a grounded, concrete, and concise overview. In initial chapters, Feldman introduces iterated functions and differential equations. He then surveys the key concepts and results to emerge from dynamical systems: chaos and the butterfly effect, deterministic randomness, bifurcations, universality, phase space, and strange attractors. Throughout, Feldman examines possible scientific implications of these phenomena for the study of complex systems, highlighting the relationships between simplicity and complexity, order and disorder. Filling the gap between popular accounts of dynamical systems and chaos and textbooks aimed at physicists and mathematicians, Chaos and Dynamical Systems will be highly useful not only to students at the undergraduate and advanced levels, but also to researchers in the natural, social, and biological sciences.

Regularity and Complexity in Dynamical Systems

Author : Albert C. J. Luo
Publisher : Springer Science & Business Media
ISBN 13 : 1461415233
Total Pages : 500 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Regularity and Complexity in Dynamical Systems by : Albert C. J. Luo

Download or read book Regularity and Complexity in Dynamical Systems written by Albert C. J. Luo and published by Springer Science & Business Media. This book was released on 2013-07-12 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Regularity and Complexity in Dynamical Systems describes periodic and chaotic behaviors in dynamical systems, including continuous, discrete, impulsive, discontinuous, and switching systems. In traditional analysis, the periodic and chaotic behaviors in continuous, nonlinear dynamical systems were extensively discussed even if unsolved. In recent years, there has been an increasing amount of interest in periodic and chaotic behaviors in discontinuous dynamical systems because such dynamical systems are prevalent in engineering. Usually, the smoothening of discontinuous dynamical system is adopted in order to use the theory of continuous dynamical systems. However, such technique cannot provide suitable results in such discontinuous systems. In this book, an alternative way is presented to discuss the periodic and chaotic behaviors in discontinuous dynamical systems.

Complex and Adaptive Dynamical Systems

Author : Claudius Gros
Publisher : Springer
ISBN 13 : 3319162659
Total Pages : 422 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Complex and Adaptive Dynamical Systems by : Claudius Gros

Download or read book Complex and Adaptive Dynamical Systems written by Claudius Gros and published by Springer. This book was released on 2015-04-01 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This primer offers readers an introduction to the central concepts that form our modern understanding of complex and emergent behavior, together with detailed coverage of accompanying mathematical methods. All calculations are presented step by step and are easy to follow. This new fourth edition has been fully reorganized and includes new chapters, figures and exercises. The core aspects of modern complex system sciences are presented in the first chapters, covering network theory, dynamical systems, bifurcation and catastrophe theory, chaos and adaptive processes, together with the principle of self-organization in reaction-diffusion systems and social animals. Modern information theoretical principles are treated in further chapters, together with the concept of self-organized criticality, gene regulation networks, hypercycles and coevolutionary avalanches, synchronization phenomena, absorbing phase transitions and the cognitive system approach to the brain. Technical course prerequisites are the standard mathematical tools for an advanced undergraduate course in the natural sciences or engineering. Each chapter includes exercises and suggestions for further reading, and the solutions to all exercises are provided in the last chapter. From the reviews of previous editions: This is a very interesting introductory book written for a broad audience of graduate students in natural sciences and engineering. It can be equally well used both for teac hing and self-education. Very well structured and every topic is illustrated with simple and motivating examples. This is a true guidebook to the world of complex nonlinear phenomena. (Ilya Pavlyukevich, Zentralblatt MATH, Vol. 1146, 2008) Claudius Gros’ Complex and Adaptive Dynamical Systems: A Primer is a welcome addition to the literature. A particular strength of the book is its emphasis on analytical techniques for studying complex systems. (David P. Feldman, Physics Today, July, 2009).

Dynamics Of Complex Systems

Author : Yaneer Bar-yam
Publisher : CRC Press
ISBN 13 : 0429717598
Total Pages : 866 pages
Book Rating : 4.4/5 (297 download)

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Book Synopsis Dynamics Of Complex Systems by : Yaneer Bar-yam

Download or read book Dynamics Of Complex Systems written by Yaneer Bar-yam and published by CRC Press. This book was released on 2019-03-04 with total page 866 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to develop models and modeling techniques that are useful when applied to all complex systems. It adopts both analytic tools and computer simulation. The book is intended for students and researchers with a variety of backgrounds.

Dynamical And Complex Systems

Author : Bullett Shaun
Publisher : World Scientific
ISBN 13 : 1786341050
Total Pages : 228 pages
Book Rating : 4.7/5 (863 download)

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Book Synopsis Dynamical And Complex Systems by : Bullett Shaun

Download or read book Dynamical And Complex Systems written by Bullett Shaun and published by World Scientific. This book was released on 2016-12-22 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book leads readers from a basic foundation to an advanced level understanding of dynamical and complex systems. It is the perfect text for graduate or PhD mathematical-science students looking for support in topics such as applied dynamical systems, Lotka–Volterra dynamical systems, applied dynamical systems theory, dynamical systems in cosmology, aperiodic order, and complex systems dynamics. Dynamical and Complex Systems is the fifth volume of the LTCC Advanced Mathematics Series. This series is the first to provide advanced introductions to mathematical science topics to advanced students of mathematics. Editor the three joint heads of the London Taught Course Centre for PhD Students in the Mathematical Sciences (LTCC), each book supports readers in broadening their mathematical knowledge outside of their immediate research disciplines while also covering specialized key areas.

Complex and Adaptive Dynamical Systems

Author : Claudius Gros
Publisher : Springer Science & Business Media
ISBN 13 : 3642365868
Total Pages : 356 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Complex and Adaptive Dynamical Systems by : Claudius Gros

Download or read book Complex and Adaptive Dynamical Systems written by Claudius Gros and published by Springer Science & Business Media. This book was released on 2013-04-23 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex system theory is rapidly developing and gaining importance, providing tools and concepts central to our modern understanding of emergent phenomena. This primer offers an introduction to this area together with detailed coverage of the mathematics involved. All calculations are presented step by step and are straightforward to follow. This new third edition comes with new material, figures and exercises. Network theory, dynamical systems and information theory, the core of modern complex system sciences, are developed in the first three chapters, covering basic concepts and phenomena like small-world networks, bifurcation theory and information entropy. Further chapters use a modular approach to address the most important concepts in complex system sciences, with the emergence and self-organization playing a central role. Prominent examples are self-organized criticality in adaptive systems, life at the edge of chaos, hypercycles and coevolutionary avalanches, synchronization phenomena, absorbing phase transitions and the cognitive system approach to the brain. Technical course prerequisites are the standard mathematical tools for an advanced undergraduate course in the natural sciences or engineering. Each chapter comes with exercises and suggestions for further reading - solutions to the exercises are provided in the last chapter. From the reviews of previous editions: This is a very interesting introductory book written for a broad audience of graduate students in natural sciences and engineering. It can be equally well used both for teaching and self-education. Very well structured and every topic is illustrated by simple and motivating examples. This is a true guidebook to the world of complex nonlinear phenomena. (Ilya Pavlyukevich, Zentralblatt MATH, Vol. 1146, 2008) "Claudius Gros's Complex and Adaptive Dynamical Systems: A Primer is a welcome addition to the literature. . A particular strength of the book is its emphasis on analytical techniques for studying complex systems. (David P. Feldman, Physics Today, July, 2009)

Complex Dynamical Systems: The Mathematics Behind the Mandelbrot and Julia Sets

Author : Robert L. Devaney
Publisher : American Mathematical Soc.
ISBN 13 : 0821802909
Total Pages : 223 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Complex Dynamical Systems: The Mathematics Behind the Mandelbrot and Julia Sets by : Robert L. Devaney

Download or read book Complex Dynamical Systems: The Mathematics Behind the Mandelbrot and Julia Sets written by Robert L. Devaney and published by American Mathematical Soc.. This book was released on 1994 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mandelbrot set has emerged as one of the most recognizable objects in mathematics. While there is no question of its beauty, relatively few people appreciate the fact that the mathematics behind such images is equally beautiful. This book presents lectures delivered during the AMS Short Course entitled Complex Dynamical Systems: The Mathematics Behind the Mandelbrot and Julia Sets, held at the Joint Mathematics Meetings in Cincinnati in January 1994. The lectures cover a wide range of topics, including the classical work of Julia and Fatou on local dynamics of analytic maps as well as recent work on the dynamics of quadratic and cubic polynomials, the geometry of Julia sets, and the structure of various parameter spaces. Among the other topics are recent results on Yoccoz puzzles and tableaux, limiting dynamics near parabolic points, the spider algorithm, extensions of the theory to rational maps, Newton's method, and entire transcendental functions. Much of the book is accessible to anyone with a background in the basics of dynamical systems and complex analysis.

Introduction to the Modern Theory of Dynamical Systems

Author : Anatole Katok
Publisher : Cambridge University Press
ISBN 13 : 9780521575577
Total Pages : 828 pages
Book Rating : 4.5/5 (755 download)

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Book Synopsis Introduction to the Modern Theory of Dynamical Systems by : Anatole Katok

Download or read book Introduction to the Modern Theory of Dynamical Systems written by Anatole Katok and published by Cambridge University Press. This book was released on 1995 with total page 828 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained comprehensive introduction to the mathematical theory of dynamical systems for students and researchers in mathematics, science and engineering.

Permutation Complexity in Dynamical Systems

Author : José Amigó
Publisher : Springer Science & Business Media
ISBN 13 : 3642040845
Total Pages : 260 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Permutation Complexity in Dynamical Systems by : José Amigó

Download or read book Permutation Complexity in Dynamical Systems written by José Amigó and published by Springer Science & Business Media. This book was released on 2010-03-20 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of permutation complexity can be envisioned as a new kind of symbolic dynamics whose basic blocks are ordinal patterns, that is, permutations defined by the order relations among points in the orbits of dynamical systems. Since its inception in 2002 the concept of permutation entropy has sparked a new branch of research in particular regarding the time series analysis of dynamical systems that capitalizes on the order structure of the state space. Indeed, on one hand ordinal patterns and periodic points are closely related, yet ordinal patterns are amenable to numerical methods, while periodicity is not. Another interesting feature is that since it can be shown that random (unconstrained) dynamics has no forbidden patterns with probability one, their existence can be used as a fingerprint to identify any deterministic origin of orbit generation. This book is primarily addressed to researchers working in the field of nonlinear dynamics and complex systems, yet will also be suitable for graduate students interested in these subjects. The presentation is a compromise between mathematical rigor and pedagogical approach. Accordingly, some of the more mathematical background needed for more in depth understanding has been shifted into the appendices.

Introduction to Complexity and Complex Systems

Author : Robert B. Northrop
Publisher : CRC Press
ISBN 13 : 1439894981
Total Pages : 551 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Introduction to Complexity and Complex Systems by : Robert B. Northrop

Download or read book Introduction to Complexity and Complex Systems written by Robert B. Northrop and published by CRC Press. This book was released on 2010-12-10 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: The boundaries between simple and complicated, and complicated and complex system designations are fuzzy and debatable, even using quantitative measures of complexity. However, if you are a biomedical engineer, a biologist, physiologist, economist, politician, stock market speculator, or politician, you have encountered complex systems. Furthermore, your success depends on your ability to successfully interact with and manage a variety of complex systems. In order not to be blindsided by unexpected results, we need a systematic, comprehensive way of analyzing, modeling, and simulating complex systems to predict non-anticipated outcomes. In its engaging first chapters, the book introduces complex systems, Campbell's Law, and the Law of Unintended Consequences, and mathematics necessary for conversations in complex systems. Subsequent chapters illustrate concepts via commonly studied biological mechanisms. The final chapters focus on higher-level complexity problems, and introduce complexity in economic systems. Designed as a reference for biologists and biological engineers, Introduction to Complexity and Complex Systems lends itself to use in a classroom course to introduce advanced students studying biomedical engineering, biophysics, or physiology to complex systems. Engaging and illustrative, this book aids scientists and decision makers in managing biological complexity and complex systems.

Advanced Topics in the Arithmetic of Elliptic Curves

Author : Joseph H. Silverman
Publisher : Springer Science & Business Media
ISBN 13 : 1461208513
Total Pages : 528 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Advanced Topics in the Arithmetic of Elliptic Curves by : Joseph H. Silverman

Download or read book Advanced Topics in the Arithmetic of Elliptic Curves written by Joseph H. Silverman and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of canonical local height functions.

Information Dynamics

Author : Harald Atmanspacher
Publisher : Springer Science & Business Media
ISBN 13 : 1489923055
Total Pages : 362 pages
Book Rating : 4.4/5 (899 download)

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Book Synopsis Information Dynamics by : Harald Atmanspacher

Download or read book Information Dynamics written by Harald Atmanspacher and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of a NATO ASI held in Irsee/Kaufbeuren, Germany, June 15--26, 1990

Science at the Frontier

Author : National Academy of Sciences
Publisher : National Academies Press
ISBN 13 : 0309045924
Total Pages : 286 pages
Book Rating : 4.3/5 (9 download)

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Book Synopsis Science at the Frontier by : National Academy of Sciences

Download or read book Science at the Frontier written by National Academy of Sciences and published by National Academies Press. This book was released on 1992-02-01 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Science at the Frontier takes you on a journey through the minds of some of the nation's leading young scientists as they explore the most exciting areas of discovery today. Based on the second Frontiers of Science symposium sponsored by the National Academy of Sciences, this book describes recent accomplishments and new directions in ten basic fields, represented by outstanding scientists convening to discuss their research. It captures the excitement and personal quality of these exchanges, sometimes pointing to surprising connections spanning the boundaries of traditional disciplines, while providing a context for the reader that explains the basic scientific framework for the fields under discussion. The volume explores: New modifications to scientific theory as geologists probe deep inside the earth and astrophysicists reach to the limits of the observable universe for answers to some of nature's most fundamental and vexing questions. The influence of research in smog formation on the public debate about how to effectively control air pollution. The increasing use of computer modeling in science, from describing the evolution of cellular automata to revealing the workings of the human brain via neural networks. The rise of dynamical systems (the study of chaotic behavior in nature) to a full-fledged science. The search to understand the regulation of gene activity and the many biological problems-such as the onset of cancer-to which it applies. Recent progress in the quest to transform what we know about photosynthesis into functional, efficient systems to tap the sun's energy. Current developments in magnetic resonance imaging and its promise for new breakthroughs in medical diagnosis. Throughout this work the reader is witness to scientific discovery and debate centered on such common concerns as the dramatic and transforming effect of computers on scientists' thinking and research; the development of more cross-disciplinary perspectives; and the very nature of the scientific enterprise itself-what it is to be part of it, and its significance for society. Science at the Frontier is must reading for informed lay readers, scientists interested in fields other than their own, and science students considering a future specialization.

Nonlinear Dynamics, Chaos, and Complexity

Author : Dimitri Volchenkov
Publisher : Springer Nature
ISBN 13 : 9811590346
Total Pages : 198 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Nonlinear Dynamics, Chaos, and Complexity by : Dimitri Volchenkov

Download or read book Nonlinear Dynamics, Chaos, and Complexity written by Dimitri Volchenkov and published by Springer Nature. This book was released on 2020-12-14 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book demonstrates how mathematical methods and techniques can be used in synergy and create a new way of looking at complex systems. It becomes clear nowadays that the standard (graph-based) network approach, in which observable events and transportation hubs are represented by nodes and relations between them are represented by edges, fails to describe the important properties of complex systems, capture the dependence between their scales, and anticipate their future developments. Therefore, authors in this book discuss the new generalized theories capable to describe a complex nexus of dependences in multi-level complex systems and to effectively engineer their important functions. The collection of works devoted to the memory of Professor Valentin Afraimovich introduces new concepts, methods, and applications in nonlinear dynamical systems covering physical problems and mathematical modelling relevant to molecular biology, genetics, neurosciences, artificial intelligence as well as classic problems in physics, machine learning, brain and urban dynamics. The book can be read by mathematicians, physicists, complex systems scientists, IT specialists, civil engineers, data scientists, urban planners, and even musicians (with some mathematical background).

Complexity Explained

Author : Peter Erdi
Publisher : Springer Science & Business Media
ISBN 13 : 3540357785
Total Pages : 397 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Complexity Explained by : Peter Erdi

Download or read book Complexity Explained written by Peter Erdi and published by Springer Science & Business Media. This book was released on 2007-11-09 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains why complex systems research is important in understanding the structure, function and dynamics of complex natural and social phenomena. It illuminates how complex collective behavior emerges from the parts of a system, due to the interaction between the system and its environment. Readers will learn the basic concepts and methods of complex system research. The book is not highly technical mathematically, but teaches and uses the basic mathematical notions of dynamical system theory, making the book useful for students of science majors and graduate courses.

Discrete Dynamical Systems

Author : Oded Galor
Publisher : Springer Science & Business Media
ISBN 13 : 3540367764
Total Pages : 159 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Discrete Dynamical Systems by : Oded Galor

Download or read book Discrete Dynamical Systems written by Oded Galor and published by Springer Science & Business Media. This book was released on 2007-05-17 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to discrete dynamical systems – a framework of analysis that is commonly used in the ?elds of biology, demography, ecology, economics, engineering, ?nance, and physics. The book characterizes the fundamental factors that govern the quantitative and qualitative trajectories of a variety of deterministic, discrete dynamical systems, providing solution methods for systems that can be solved analytically and methods of qualitative analysis for those systems that do not permit or necessitate an explicit solution. The analysis focuses initially on the characterization of the factors that govern the evolution of state variables in the elementary context of one-dimensional, ?rst-order, linear, autonomous systems. The f- damental insights about the forces that a?ect the evolution of these - ementary systems are subsequently generalized, and the determinants of the trajectories of multi-dimensional, nonlinear, higher-order, non- 1 autonomous dynamical systems are established. Chapter 1 focuses on the analysis of the evolution of state variables in one-dimensional, ?rst-order, autonomous systems. It introduces a method of solution for these systems, and it characterizes the traj- tory of a state variable, in relation to a steady-state equilibrium of the system, examining the local and global (asymptotic) stability of this steady-state equilibrium. The ?rst part of the chapter characterizes the factors that determine the existence, uniqueness and stability of a steady-state equilibrium in the elementary context of one-dimensional, ?rst-order, linear autonomous systems.