Chaos in Real Data studies the range of data analytic techniques available to study nonlinear population dynamics for ecological time series. Several case studies are studied using typically short and noisy population data from field and laboratory. A range of modern approaches, such as response surface methodology and mechanistic mathematical modelling, are applied to several case studies. Experts honestly appraise how well these methods have performed on their data. The accessible style of the book ensures its readability for non-quantitative biologists. The data remain available, as benchmarks for future study, on the worldwide web.

The study of chaotic systems has become a major scientific pursuit in recent years, shedding light on the apparently random behaviour observed in fields as diverse as climatology and mechanics. InThe Essence of Chaos Edward Lorenz, one of the founding fathers of Chaos and the originator of its seminal concept of the Butterfly Effect, presents his own landscape of our current understanding of the field. Lorenz presents everyday examples of chaotic behaviour, such as the toss of a coin, the pinball's path, the fall of a leaf, and explains in elementary mathematical strms how their essentially chaotic nature can be understood. His principal example involved the construction of a model of a board sliding down a ski slope. Through this model Lorenz illustrates chaotic phenomena and the related concepts of bifurcation and strange attractors. He also provides the context in which chaos can be related to the similarly emergent fields of nonlinearity, complexity and fractals. As an early pioneer of chaos, Lorenz also provides his own story of the human endeavour in developing this new field. He describes his initial encounters with chaos through his study of climate and introduces many of the personalities who contributed early breakthroughs. His seminal paper, "Does the Flap of a Butterfly's Wing in Brazil Set Off a Tornado in Texas?" is published for the first time.

Chaos and complexity explained, with illuminating examples ranging from unpredictable pendulums to London's wobbly Millennium Bridge. The math we are taught in school is precise and only deals with simple situations. Reality is far more complex. Trying to understand a system with multiple interacting components—the weather, for example, or the human body, or the stock market—means dealing with two factors: chaos and complexity. If we don't understand these two essential subjects, we can't understand the real world. In Everyday Chaos, Brian Clegg explains chaos and complexity for the general reader, with an accessible, engaging text and striking full-color illustrations. By chaos, Clegg means a system where complex interactions make predicting long-term outcomes nearly impossible; complexity means complex interacting systems that have new emergent properties that make them more than the sum of their parts. Clegg illustrates these phenomena with discussions of predictable randomness, the power of probability, and the behavior of pendulums. He describes what Newton got wrong about gravity; how feedback kept steam engines from exploding; and why weather produces chaos. He considers the stock market, politics, bestseller lists, big data, and London's wobbling Millennium Bridge as examples of chaotic systems, and he explains how a better understanding of chaos helps scientists predict more accurately the risk of catastrophic Earth-asteroid collisions. We learn that our brains are complex, self-organizing systems; that the structure of snowflakes exemplifies emergence; and that life itself has been shown to be an emergent property of a complex system.

Make. More. Future. Artificial intelligence, big data, modern science, and the internet are all revealing a fundamental truth: The world is vastly more complex and unpredictable than we've allowed ourselves to see. Now that technology is enabling us to take advantage of all the chaos it's revealing, our understanding of how things happen is changing--and with it our deepest strategies for predicting, preparing for, and managing our world. This affects everything, from how we approach our everyday lives to how we make moral decisions and how we run our businesses. Take machine learning, which makes better predictions about weather, medical diagnoses, and product performance than we do--but often does so at the expense of our understanding of how it arrived at those predictions. While this can be dangerous, accepting it is also liberating, for it enables us to harness the complexity of an immense amount of data around us. We are also turning to strategies that avoid anticipating the future altogether, such as A/B testing, Minimum Viable Products, open platforms, and user-modifiable video games. We even take for granted that a simple hashtag can organize unplanned, leaderless movements such as #MeToo. Through stories from history, business, and technology, philosopher and technologist David Weinberger finds the unifying truths lying below the surface of the tools we take for granted--and a future in which our best strategy often requires holding back from anticipating and instead creating as many possibilities as we can. The book’s imperative for business and beyond is simple: Make. More. Future. The result is a world no longer focused on limitations but optimized for possibilities.

This book provides techniques to become numerically literate and able to understand and digest data.

The first edition of this book was originally published in 1985 under the ti tle "Probabilistic Properties of Deterministic Systems. " In the intervening years, interest in so-called "chaotic" systems has continued unabated but with a more thoughtful and sober eye toward applications, as befits a ma turing field. This interest in the serious usage of the concepts and techniques of nonlinear dynamics by applied scientists has probably been spurred more by the availability of inexpensive computers than by any other factor. Thus, computer experiments have been prominent, suggesting the wealth of phe nomena that may be resident in nonlinear systems. In particular, they allow one to observe the interdependence between the deterministic and probabilistic properties of these systems such as the existence of invariant measures and densities, statistical stability and periodicity, the influence of stochastic perturbations, the formation of attractors, and many others. The aim of the book, and especially of this second edition, is to present recent theoretical methods which allow one to study these effects. We have taken the opportunity in this second edition to not only correct the errors of the first edition, but also to add substantially new material in five sections and a new chapter.

This text aims to bridge the gap between non-mathematical popular treatments and the distinctly mathematical publications that non- mathematicians find so difficult to penetrate. The author provides understandable derivations or explanations of many key concepts, such as Kolmogrov-Sinai entropy, dimensions, Fourier analysis, and Lyapunov exponents.

Chaos in Ecology is a convincing demonstration of chaos in a biological population. The book synthesizes an ecologically focused interdisciplinary blend of non-linear dynamics theory, statistics, and experimentation yielding results of uncommon clarity and rigor. Topics include fundamental issues that are of general and widespread importance to population biology and ecology. Detailed descriptions are included of the mathematical, statistical, and experimental steps they used to explore nonlinear dynamics in ecology. Beginning with a brief overview of chaos theory and its implications for ecology. The book continues by deriving and rigorously testing a mathematical model that is closely wedded to biological mechanisms of their research organism. Therefrom were generated a variety of predictions that are fundamental to chaos theory and experiments were designed and analyzed to test those predictions. Discussion of patterns in chaos and how they can be investigated using real data follows and book ends with a discussion of the salient lessons learned from this research program Book jacket.

In this volume, leading experts present current achievements in the forefront of research in the challenging field of chaos in circuits and systems, with emphasis on engineering perspectives, methodologies, circuitry design techniques, and potential applications of chaos and bifurcation. A combination of overview, tutorial and technical articles, the book describes state-of-the-art research on significant problems in this field. It is suitable for readers ranging from graduate students, university professors, laboratory researchers and industrial practitioners to applied mathematicians and physicists in electrical, electronic, mechanical, physical, chemical and biomedical engineering and science.

This book focuses on explaining the fundamentals of the physics and mathematics of chaotic phenomena by studying examples from one-dimensional maps and simple differential equations. It is helpful for postgraduate students and researchers in mathematics, physics and other areas of science.