Exploring Discrete Dynamics
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Exploring Discrete Dynamics
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Author : Andrew Wuensche
language : en
Publisher: Luniver Press
Release Date : 2011
Exploring Discrete Dynamics written by Andrew Wuensche and has been published by Luniver Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Computers categories.
EXPLORING DISCRETE DYNAMICS is a comprehensive guide to studying cellular automata and discrete dynamical networks with the classic software Discrete Dynamics Laboratory (DDLab). These collective networks are at the core of complexity and emergent self-organisation. With interactive graphics, DDLab is able to explore an huge diversity of behaviour -- mostly terra incognita -- space-time patters, but also basins of attraction, mathematical objects representing the convergent flow in state-space. Applications range within physics, mathematics, biology, cognition, society, economics and computation, and more specifically in neural and genetic networks, artificial life, and a theory of memory.
Exploring Discrete Dynamics 2nd Editiion The Ddlab Manual
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Author : Andrew Wuensche
language : en
Publisher:
Release Date : 2016-06-15
Exploring Discrete Dynamics 2nd Editiion The Ddlab Manual written by Andrew Wuensche and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-15 with Computers categories.
EXPLORING DISCRETE DYNAMICS (second edition) is a comprehensive guide to studying cellular automata and discrete dynamical networks with the classic software Discrete Dynamics Laboratory (DDLab), widely used in research and education. These collective networks are at the core of complexity and emergent self-organisation. With interactive graphics, DDLab is able to explore a huge diversity of behaviour, mostly terra incognita -- space-time patterns, and basins of attraction -- mathematical objects representing the convergent flow in state-space. Applications range within physics, mathematics, biology, cognition, society, economics and computation, and more specifically in neural and genetic networks, artificial life, and theories of memory. This second edition covers many new features. Advance Praise by Stuart Kauffman The great John von Neumann invented cellular automata. These discrete state finite automata have become a mainstay in the study of complex systems, exhibiting order, criticality, and chaos. Andy Wuensche's "Exploring Discrete Dynamics" 2016, is by far the most advanced tool for simulating such systems and has become widely important in the field of complexity. FIRST EDITION REVIEWS Andrew Wuensche has, in an important sense, done more than anyone to enable the study of discrete dynamical systems such as cellular automata and random Boolean nets. Wuensche derived the mathematical means to compute the "predecessor" states that flow to a successor state. Thereby he opened the door to study the entire state space flow of discrete dynamical systems. DDLab is a marvellous and useful tool for all of us fascinated by discrete dynamical systems and what they may tell us of mathematics and the world. STUART KAUFFMAN, author of "The Origins of Order" Tampere University of Technology, Finland. There is a whole universe of complexity that is captured by discrete dynamical systems, which have been widely used as a powerful framework to understand reality from different perspectives. Exploring Discrete Dynamics is a great example of how to dive in this neverending universe. A careful, compelling and detailed presentation of examples and methods will help both beginners and scholars to get into this fascinating field." RICARD SOLE, Author of "Signs of Life" Complex Systems Lab, Universitat Pompeu Fabra, Barcelona.
Discovering Discrete Dynamical Systems
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Author : Aimee Johnson
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-12-31
Discovering Discrete Dynamical Systems written by Aimee Johnson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-31 with Mathematics categories.
Discovering Discrete Dynamical Systems is a mathematics textbook designed for use in a student-led, inquiry-based course for advanced mathematics majors. Fourteen modules each with an opening exploration, a short exposition and related exercises, and a concluding project guide students to self-discovery on topics such as fixed points and their classifications, chaos and fractals, Julia and Mandelbrot sets in the complex plane, and symbolic dynamics. Topics have been carefully chosen as a means for developing student persistence and skill in exploration, conjecture, and generalization while at the same time providing a coherent introduction to the fundamentals of discrete dynamical systems. This book is written for undergraduate students with the prerequisites for a first analysis course, and it can easily be used by any faculty member in a mathematics department, regardless of area of expertise. Each module starts with an exploration in which the students are asked an open-ended question. This allows the students to make discoveries which lead them to formulate the questions that will be addressed in the exposition and exercises of the module. The exposition is brief and has been written with the intent that a student who has taken, or is ready to take, a course in analysis can read the material independently. The exposition concludes with exercises which have been designed to both illustrate and explore in more depth the ideas covered in the exposition. Each module concludes with a project in which students bring the ideas from the module to bear on a more challenging or in-depth problem. A section entitled "To the Instructor" includes suggestions on how to structure a course in order to realize the inquiry-based intent of the book. The book has also been used successfully as the basis for an independent study course and as a supplementary text for an analysis course with traditional content.
Discrete Dynamical Systems
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Author : Oded Galor
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-17
Discrete Dynamical Systems written by Oded Galor and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-17 with Business & Economics categories.
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.
Differential Equations Dynamical Systems And An Introduction To Chaos
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Author : Morris W. Hirsch
language : en
Publisher: Academic Press
Release Date : 2004
Differential Equations Dynamical Systems And An Introduction To Chaos written by Morris W. Hirsch and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Business & Economics categories.
Thirty years in the making, this revised text by three of the world's leading mathematicians covers the dynamical aspects of ordinary differential equations. it explores the relations between dynamical systems and certain fields outside pure mathematics, and has become the standard textbook for graduate courses in this area. The Second Edition now brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra. The authors are tops in the field of advanced mathematics, including Steve Smale who is a recipient of.
Techniques In Mathematical Modelling
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Author : Gautami Devar
language : en
Publisher: Educohack Press
Release Date : 2025-02-20
Techniques In Mathematical Modelling written by Gautami Devar and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.
"Techniques in Mathematical Modelling" is a comprehensive textbook designed to provide students, researchers, and practitioners with a solid foundation in the principles, techniques, and applications of mathematical modelling. We cover a wide range of topics, from fundamental concepts and analytical techniques to validation methods and emerging trends. Each chapter includes practical examples, case studies, and exercises to reinforce learning and demonstrate real-world applications. Our book emphasizes the interdisciplinary nature of mathematical modelling, with applications in physics, biology, economics, engineering, social sciences, and more. We encourage hands-on learning through practical exercises, simulations, and projects, allowing readers to apply theoretical concepts to real-world scenarios. Additionally, we explore emerging trends and challenges in the field, including advancements in computational techniques, data analytics, and interdisciplinary collaborations. Written in clear and accessible language, "Techniques in Mathematical Modelling" caters to readers with varying levels of mathematical background, making it suitable for undergraduate and graduate students as well as professionals.
Advances In Cellular Automata
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Author : Andrew Adamatzky
language : en
Publisher: Springer Nature
Release Date : 2025-04-26
Advances In Cellular Automata written by Andrew Adamatzky and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-26 with Computers categories.
This book embarks on a journey through the captivating universe of cellular automata and discover its distinct realm, characterised by discrete time, space, and states, where cells form regular patterns and offer insights into complex systems across various domains. From theoretical foundations to practical applications, each chapter unveils innovative ideas and implementations, from solving initial value problems to exploring reversible computing and real-time pattern generation. Explore hyperbolic spaces, analyse elementary automata, and delve into network growth dynamics. Shedding light on synchronisation, control, and computational structures, this book is an invaluable resource for computer scientists, modellers, mathematicians, engineers, physicists, and professionals across disciplines. Immerse yourself in the intricate complexities and boundless potential of cellular automata, whether unravelling pedestrian dynamics or exploring cryptographic applications.
Designing Beauty The Art Of Cellular Automata
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Author : Andrew Adamatzky
language : en
Publisher: Springer
Release Date : 2016-01-05
Designing Beauty The Art Of Cellular Automata written by Andrew Adamatzky and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-05 with Technology & Engineering categories.
This fascinating, colourful book offers in-depth insights and first-hand working experiences in the production of art works, using simple computational models with rich morphological behaviour, at the edge of mathematics, computer science, physics and biology. It organically combines ground breaking scientific discoveries in the theory of computation and complex systems with artistic representations of the research results. In this appealing book mathematicians, computer scientists, physicists, and engineers brought together marvelous and esoteric patterns generated by cellular automata, which are arrays of simple machines with complex behavior. Configurations produced by cellular automata uncover mechanics of dynamic patterns formation, their propagation and interaction in natural systems: heart pacemaker, bacterial membrane proteins, chemical rectors, water permeation in soil, compressed gas, cell division, population dynamics, reaction-diffusion media and self-organisation. The book inspires artists to take on cellular automata as a tool of creativity and it persuades scientists to convert their research results into the works of art. The book is lavishly illustrated with visually attractive examples, presented in a lively and easily accessible manner.
An Exploration Of Dynamical Systems And Chaos
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Author : John H. Argyris
language : en
Publisher: Springer
Release Date : 2015-04-24
An Exploration Of Dynamical Systems And Chaos written by John H. Argyris and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-24 with Technology & Engineering categories.
This book is conceived as a comprehensive and detailed text-book on non-linear dynamical systems with particular emphasis on the exploration of chaotic phenomena. The self-contained introductory presentation is addressed both to those who wish to study the physics of chaotic systems and non-linear dynamics intensively as well as those who are curious to learn more about the fascinating world of chaotic phenomena. Basic concepts like Poincaré section, iterated mappings, Hamiltonian chaos and KAM theory, strange attractors, fractal dimensions, Lyapunov exponents, bifurcation theory, self-similarity and renormalisation and transitions to chaos are thoroughly explained. To facilitate comprehension, mathematical concepts and tools are introduced in short sub-sections. The text is supported by numerous computer experiments and a multitude of graphical illustrations and colour plates emphasising the geometrical and topological characteristics of the underlying dynamics. This volume is a completely revised and enlarged second edition which comprises recently obtained research results of topical interest, and has been extended to include a new section on the basic concepts of probability theory. A completely new chapter on fully developed turbulence presents the successes of chaos theory, its limitations as well as future trends in the development of complex spatio-temporal structures. "This book will be of valuable help for my lectures" Hermann Haken, Stuttgart "This text-book should not be missing in any introductory lecture on non-linear systems and deterministic chaos" Wolfgang Kinzel, Würzburg “This well written book represents a comprehensive treatise on dynamical systems. It may serve as reference book for the whole field of nonlinear and chaotic systems and reports in a unique way on scientific developments of recent decades as well as important applications.” Joachim Peinke, Institute of Physics, Carl-von-Ossietzky University Oldenburg, Germany
Astrodynamics Network Astronet Ii
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Author : Gerard Gómez
language : en
Publisher: Springer
Release Date : 2016-07-29
Astrodynamics Network Astronet Ii written by Gerard Gómez and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-29 with Science categories.
These are the proceedings of the "AstroNet-II International Final Conference". This conference was one of the last milestones of the Marie-Curie Research Training Network on Astrodynamics "AstroNet-II", that has been funded by the European Commission under the Seventh Framework Programme. The aim of the conference, and thus this book, is to communicate work on astrodynamics problems to an international and specialised audience. The results are presented by both members of the network and invited specialists. The topics include: trajectory design and control, attitude control, structural flexibility of spacecraft and formation flying. The book addresses a readership across the traditional boundaries between mathematics, engineering and industry by offering an interdisciplinary and multisectorial overview of the field.