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Author: Mike R. Jeffrey
Publisher: Springer
ISBN: 3030021076
Category : Mathematics
Languages : en
Pages : 521
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Book Description
The dream of mathematical modeling is of systems evolving in a continuous, deterministic, predictable way. Unfortunately continuity is lost whenever the `rules of the game' change, whether a change of behavioural regime, or a change of physical properties. From biological mitosis to seizures. From rattling machine parts to earthquakes. From individual decisions to economic crashes. Where discontinuities occur, determinacy is inevitably lost. Typically the physical laws of such change are poorly understood, and too ill-defined for standard mathematics. Discontinuities offer a way to make the bounds of scientific knowledge a part of the model, to analyse a system with detail and rigour, yet still leave room for uncertainty. This is done without recourse to stochastic modeling, instead retaining determinacy as far as possible, and focussing on the geometry of the many outcomes that become possible when it breaks down. In this book the foundations of `piecewise-smooth dynamics' theory are rejuvenated, given new life through the lens of modern nonlinear dynamics and asymptotics. Numerous examples and exercises lead the reader through from basic to advanced analytical methods, particularly new tools for studying stability and bifurcations. The book is aimed at scientists and engineers from any background with a basic grounding in calculus and linear algebra. It seeks to provide an invaluable resource for modeling discontinuous systems, but also to empower the reader to develop their own novel models and discover as yet unknown phenomena.
Author: Mike R. Jeffrey
Publisher: Springer
ISBN: 3030021076
Category : Mathematics
Languages : en
Pages : 521
Get Book
Book Description
The dream of mathematical modeling is of systems evolving in a continuous, deterministic, predictable way. Unfortunately continuity is lost whenever the `rules of the game' change, whether a change of behavioural regime, or a change of physical properties. From biological mitosis to seizures. From rattling machine parts to earthquakes. From individual decisions to economic crashes. Where discontinuities occur, determinacy is inevitably lost. Typically the physical laws of such change are poorly understood, and too ill-defined for standard mathematics. Discontinuities offer a way to make the bounds of scientific knowledge a part of the model, to analyse a system with detail and rigour, yet still leave room for uncertainty. This is done without recourse to stochastic modeling, instead retaining determinacy as far as possible, and focussing on the geometry of the many outcomes that become possible when it breaks down. In this book the foundations of `piecewise-smooth dynamics' theory are rejuvenated, given new life through the lens of modern nonlinear dynamics and asymptotics. Numerous examples and exercises lead the reader through from basic to advanced analytical methods, particularly new tools for studying stability and bifurcations. The book is aimed at scientists and engineers from any background with a basic grounding in calculus and linear algebra. It seeks to provide an invaluable resource for modeling discontinuous systems, but also to empower the reader to develop their own novel models and discover as yet unknown phenomena.
Author: G. Schreyögg
Publisher: Springer
ISBN: 0230274072
Category : Business & Economics
Languages : en
Pages : 265
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Book Description
The theory of path dependence continues to attract great interest in a range of disciplines. An increasing number of scholars have started to explicitly use this theory for studying organizational inertia and institutional rigidities. This volume presents a collection of papers from various international conferences that address these issues.
Author: Christos Volos
Publisher: MDPI
ISBN: 3038978981
Category : Technology & Engineering
Languages : en
Pages : 290
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Book Description
In recent years, entropy has been used as a measure of the degree of chaos in dynamical systems. Thus, it is important to study entropy in nonlinear systems. Moreover, there has been increasing interest in the last few years regarding the novel classification of nonlinear dynamical systems including two kinds of attractors: self-excited attractors and hidden attractors. The localization of self-excited attractors by applying a standard computational procedure is straightforward. In systems with hidden attractors, however, a specific computational procedure must be developed, since equilibrium points do not help in the localization of hidden attractors. Some examples of this kind of system are chaotic dynamical systems with no equilibrium points; with only stable equilibria, curves of equilibria, and surfaces of equilibria; and with non-hyperbolic equilibria. There is evidence that hidden attractors play a vital role in various fields ranging from phase-locked loops, oscillators, describing convective fluid motion, drilling systems, information theory, cryptography, and multilevel DC/DC converters. This Special Issue is a collection of the latest scientific trends on the advanced topics of dynamics, entropy, fractional order calculus, and applications in complex systems with self-excited attractors and hidden attractors.
Author: Klaus P Horn
Publisher: Carl-Auer Verlag
ISBN: 3849781690
Category : Psychology
Languages : en
Pages : 249
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Book Description
The company isn't booming, the customers are drifting away, innovation is at a standstill – What's wrong? A rational analysis can provide you with pieces of the problem, but never the whole picture. Systemic constellations give you the missing link. Success with this method in companies such as Daimler-Chrysler, IBM, and BMW has contributed to a booming interest in Europe. When the systemic structure of a team, company or market becomes clear, it is obvious what has to happen next. Individuals who are not involved in the problem situation are used to represent people or parts of the company and a trained consultant uses feedback from the representatives to reveal hidden dynamics and point to solutions. Anyone in a position of responsibility in industry or government, or an organisation in health education or welfare can profit from this book. It is easy to read and practical, with case examples and short summaries for quick scanning. "A totally obscure situation suddenly became as clear as day. How come we couldn't see the obvious before?! For all of our company leaders it was a total revelation." O. Wassermann, CEO of Wassermann AG/Swisslog, Munich, Germany
Author: Frasca Mattia
Publisher: World Scientific
ISBN: 9813227257
Category : Technology & Engineering
Languages : en
Pages : 148
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Book Description
This book focuses on a class of uncertain systems that are called imperfect, and shows how much systems can regularly work if an appropriate control strategy is adopted. Along with some practical well studied examples, a formalization of the models for imperfect system is considered and a control strategy is proposed. Experimental case studies on electromechanical systems are also included. New concepts, experimental innovative circuits and laboratory details allow the reader to implement at low cost the outlined strategy. Emergent topics in nonlinear device realization are emphasized with the aim to allow researchers and students to perform experiments with large scale electromechanical systems. Moreover, the possibility of using imperfections and noise to generate nonlinear strange behavior is discussed.
Author: Faith Ralston
Publisher: Amacom Books
ISBN: 9780814402726
Category : Business & Economics
Languages : en
Pages : 176
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Book Description
This guide offers practical advice for turning strong feelings into a positive force for building a more vigorous organization and enhancing your own job satisfaction. It's packed with examples, exercises, and tools for training that will help you improve individual and team performance; reduce interpersonal conflict and barriers to cooperation; integrate feelings and facts when making business decisions; develop managerial skills of facilitation, communication, and leadership; and motivate employees to take more responsibility. Emotional needs always express themselves one way or another, even in a business environment, says the author. Understanding the "Eight Principles of Emotions" described here will give you unique insights into why people behave the way they do. Armed with this valuable knowledge, you'll learn to deal with typical workplace issues and situations.
Author: J. F. Gómez-Aguilar
Publisher: CRC Press
ISBN: 100059761X
Category : Mathematics
Languages : en
Pages : 511
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Book Description
Applications of Fractional Calculus to Modeling in Dynamics and Chaos aims to present novel developments, trends, and applications of fractional-order derivatives with power law and Mittag-Leffler kernel in the areas of chemistry, mechanics, chaos, epidemiology, fluid mechanics, modeling, and engineering. Non-singular and non-local fractional-order derivatives have been applied in different chapters to describe complex problems. The book offers theory and practical applications for the solutions of real-life problems and will be of interest to graduate-level students, educators, researchers, and scientists interested in mathematical modeling and its diverse applications. Features Discusses real-world problems, theory, and applications Covers new developments and advances in the various areas of nonlinear dynamics, signal processing, and chaos Suitable to teach master’s and/or PhD-level graduate students, and can be used by researchers, from any field of the social, health, and physical sciences
Author: Gustavo Deco
Publisher: Springer Science & Business Media
ISBN: 1461301270
Category : Computers
Languages : en
Pages : 289
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Book Description
This book offers a new, theoretical approach to information dynamics, i.e., information processing in complex dynamical systems. The presentation establishes a consistent theoretical framework for the problem of discovering knowledge behind empirical, dynamical data and addresses applications in information processing and coding in dynamical systems. This will be an essential reference for those in neural computing, information theory, nonlinear dynamics and complex systems modeling.
Author: Anthony G. O'Farrell
Publisher: Cambridge University Press
ISBN: 1316195767
Category : Mathematics
Languages : en
Pages : 295
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Book Description
Reversibility is a thread woven through many branches of mathematics. It arises in dynamics, in systems that admit a time-reversal symmetry, and in group theory where the reversible group elements are those that are conjugate to their inverses. However, the lack of a lingua franca for discussing reversibility means that researchers who encounter the concept may be unaware of related work in other fields. This text is the first to make reversibility the focus of attention. The authors fix standard notation and terminology, establish the basic common principles, and illustrate the impact of reversibility in such diverse areas as group theory, differential and analytic geometry, number theory, complex analysis and approximation theory. As well as showing connections between different fields, the authors' viewpoint reveals many open questions, making this book ideal for graduate students and researchers. The exposition is accessible to readers at the advanced undergraduate level and above.
Author: Mike R. Jeffrey
Publisher: Springer Nature
ISBN: 3030359875
Category : Mathematics
Languages : en
Pages : 104
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Book Description
This volume looks at the study of dynamical systems with discontinuities. Discontinuities arise when systems are subject to switches, decisions, or other abrupt changes in their underlying properties that require a ‘non-smooth’ definition. A review of current ideas and introduction to key methods is given, with a view to opening discussion of a major open problem in our fundamental understanding of what nonsmooth models are. What does a nonsmooth model represent: an approximation, a toy model, a sophisticated qualitative capturing of empirical law, or a mere abstraction? Tackling this question means confronting rarely discussed indeterminacies and ambiguities in how we define, simulate, and solve nonsmooth models. The author illustrates these with simple examples based on genetic regulation and investment games, and proposes precise mathematical tools to tackle them. The volume is aimed at students and researchers who have some experience of dynamical systems, whether as a modelling tool or studying theoretically. Pointing to a range of theoretical and applied literature, the author introduces the key ideas needed to tackle nonsmooth models, but also shows the gaps in understanding that all researchers should be bearing in mind. Mike Jeffrey is a researcher and lecturer at the University of Bristol with a background in mathematical physics, specializing in dynamics, singularities, and asymptotics.
