Introduction To Mathematical Modeling And Chaotic Dynamics

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Introduction to Mathematical Modeling and Chaotic Dynamics

Ranjit Kumar Upadhyay,Satteluri R. K. Iyengar
Introduction to Mathematical Modeling and Chaotic Dynamics Book PDF

Author : Ranjit Kumar Upadhyay,Satteluri R. K. Iyengar
Publisher : CRC Press
Page : 363 pages
File Size : 47,6 Mb
Release : 2013-07-23
Category : Mathematics
ISBN : 9781439898871

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Introduction to Mathematical Modeling and Chaotic Dynamics by Ranjit Kumar Upadhyay,Satteluri R. K. Iyengar Pdf

Introduction to Mathematical Modeling and Chaotic Dynamics focuses on mathematical models in natural systems, particularly ecological systems. Most of the models presented are solved using MATLAB®. The book first covers the necessary mathematical preliminaries, including testing of stability. It then describes the modeling of systems from natural science, focusing on one- and two-dimensional continuous and discrete time models. Moving on to chaotic dynamics, the authors discuss ways to study chaos, types of chaos, and methods for detecting chaos. They also explore chaotic dynamics in single and multiple species systems. The text concludes with a brief discussion on models of mechanical systems and electronic circuits. Suitable for advanced undergraduate and graduate students, this book provides a practical understanding of how the models are used in current natural science and engineering applications. Along with a variety of exercises and solved examples, the text presents all the fundamental concepts and mathematical skills needed to build models and perform analyses.

Introduction to Mathematical Modeling Using Discrete Dynamical Systems

Frederick R. Marotto
Introduction to Mathematical Modeling Using Discrete Dynamical Systems Book PDF

Author : Frederick R. Marotto
Publisher : Cengage Learning
Page : 400 pages
File Size : 53,7 Mb
Release : 2005-09-01
Category : Discrete-time systems
ISBN : 0495018651

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Introduction to Mathematical Modeling Using Discrete Dynamical Systems by Frederick R. Marotto Pdf

Using discrete dynamical systems, this book introduces powerful mathematical modeling techniques, both standard analytical and modern computational, to students in mathematics, the natural sciences, and the social sciences. With minimal mathematical background, students will quickly progress from the traditional study of exponential growth and decay that simple linear equations always exhibit, to an investigation of recently discovered chaotic dynamics often associated with nonlinear systems. A wide diversity of applications demonstrates the usefulness and relevance of topics that have often been viewed as excessively theoretical or abstract, such as sequences, limits, linear algebra, complex variables, and more. By taking advantage of discrete dynamical systems, students will have the opportunity to experience some fascinating areas of mathematical discovery.

Chaos

Kathleen Alligood,Tim Sauer,J.A. Yorke
Chaos Book PDF

Author : Kathleen Alligood,Tim Sauer,J.A. Yorke
Publisher : Springer
Page : 620 pages
File Size : 40,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642592812

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Chaos by Kathleen Alligood,Tim Sauer,J.A. Yorke Pdf

BACKGROUND Sir Isaac Newton hrought to the world the idea of modeling the motion of physical systems with equations. It was necessary to invent calculus along the way, since fundamental equations of motion involve velocities and accelerations, of position. His greatest single success was his discovery that which are derivatives the motion of the planets and moons of the solar system resulted from a single fundamental source: the gravitational attraction of the hodies. He demonstrated that the ohserved motion of the planets could he explained hy assuming that there is a gravitational attraction he tween any two ohjects, a force that is proportional to the product of masses and inversely proportional to the square of the distance between them. The circular, elliptical, and parabolic orhits of astronomy were v INTRODUCTION no longer fundamental determinants of motion, but were approximations of laws specified with differential equations. His methods are now used in modeling motion and change in all areas of science. Subsequent generations of scientists extended the method of using differ ential equations to describe how physical systems evolve. But the method had a limitation. While the differential equations were sufficient to determine the behavior-in the sense that solutions of the equations did exist-it was frequently difficult to figure out what that behavior would be. It was often impossible to write down solutions in relatively simple algebraic expressions using a finite number of terms. Series solutions involving infinite sums often would not converge beyond some finite time.

Introduction to Mathematical Modeling

Mayer Humi
Introduction to Mathematical Modeling Book PDF

Author : Mayer Humi
Publisher : CRC Press
Page : 500 pages
File Size : 40,5 Mb
Release : 2017-09-19
Category : Mathematics
ISBN : 9781498728010

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Introduction to Mathematical Modeling by Mayer Humi Pdf

Introduction to Mathematical Modeling helps students master the processes used by scientists and engineers to model real-world problems, including the challenges posed by space exploration, climate change, energy sustainability, chaotic dynamical systems and random processes. Primarily intended for students with a working knowledge of calculus but minimal training in computer programming in a first course on modeling, the more advanced topics in the book are also useful for advanced undergraduate and graduate students seeking to get to grips with the analytical, numerical, and visual aspects of mathematical modeling, as well as the approximations and abstractions needed for the creation of a viable model.

Differential Dynamical Systems, Revised Edition

James D. Meiss
Differential Dynamical Systems Revised Edition Book PDF

Author : James D. Meiss
Publisher : SIAM
Page : 392 pages
File Size : 50,7 Mb
Release : 2017-01-24
Category : Mathematics
ISBN : 9781611974645

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Differential Dynamical Systems, Revised Edition by James D. Meiss Pdf

Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics.? Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple?, Mathematica?, and MATLAB? software to give students practice with computation applied to dynamical systems problems.

A Mathematical Modeling Approach from Nonlinear Dynamics to Complex Systems

Elbert E. N. Macau
A Mathematical Modeling Approach from Nonlinear Dynamics to Complex Systems Book PDF

Author : Elbert E. N. Macau
Publisher : Springer
Page : 228 pages
File Size : 40,6 Mb
Release : 2018-06-14
Category : Technology & Engineering
ISBN : 9783319785127

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A Mathematical Modeling Approach from Nonlinear Dynamics to Complex Systems by Elbert E. N. Macau Pdf

This book collects recent developments in nonlinear and complex systems. It provides up-to-date theoretic developments and new techniques based on a nonlinear dynamical systems approach that can be used to model and understand complex behavior in nonlinear dynamical systems. It covers symmetry groups, conservation laws, risk reduction management, barriers in Hamiltonian systems, and synchronization and chaotic transient. Illustrating mathematical modeling applications to nonlinear physics and nonlinear engineering, the book is ideal for academic and industrial researchers concerned with machinery and controls, manufacturing, and controls. · Introduces new concepts for understanding and modeling complex systems; · Explains risk reduction management in complex systems; · Examines the symmetry group approach to understanding complex systems; · Illustrates the relation between transient chaos and crises.

Introduction to the Simulation of Dynamics Using Simulink

Michael A. Gray
Introduction to the Simulation of Dynamics Using Simulink Book PDF

Author : Michael A. Gray
Publisher : CRC Press
Page : 326 pages
File Size : 47,6 Mb
Release : 2010-07-02
Category : Mathematics
ISBN : 9781439818978

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Introduction to the Simulation of Dynamics Using Simulink by Michael A. Gray Pdf

Designed for undergraduate students in the general science, engineering, and mathematics community, Introduction to the Simulation of Dynamics Using Simulink® shows how to use the powerful tool of Simulink to investigate and form intuitions about the behavior of dynamical systems. Requiring no prior programming experience, it clearly explains how to transition from physical models described by mathematical equations directly to executable Simulink simulations. Teaches students how to model and explore the dynamics of systems Step by step, the author presents the basics of building a simulation in Simulink. He begins with finite difference equations and simple discrete models, such as annual population models, to introduce the concept of state. The text then covers ordinary differential equations, numerical integration algorithms, and time-step simulation. The final chapter offers overviews of some advanced topics, including the simulation of chaotic dynamics and partial differential equations. A one-semester undergraduate course on simulation Written in an informal, accessible style, this guide includes many diagrams and graphics as well as exercises embedded within the text. It also draws on numerous examples from the science, engineering, and technology fields. The book deepens students’ understanding of simulated systems and prepares them for advanced and specialized studies in simulation. Ancillary materials are available at http://nw08.american.edu/~gray

Chaotic Dynamics of Nonlinear Systems

S. Neil Rasband
Chaotic Dynamics of Nonlinear Systems Book PDF

Author : S. Neil Rasband
Publisher : Courier Dover Publications
Page : 240 pages
File Size : 45,8 Mb
Release : 2015-07-20
Category : Science
ISBN : 9780486805771

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Chaotic Dynamics of Nonlinear Systems by S. Neil Rasband Pdf

Written when the young science of chaos was gaining a foothold in the scientific community, this book introduces the field's concepts, applications, theory, and technique. Suitable for advanced undergraduates and graduate students, researchers, and teachers of mathematics, physics, and engineering, the text's major prerequisite is familiarity with differential equations and linear vector spaces. Author S. Neil Rasband discusses the major models for the transitions to chaos exhibited by dynamic systems, introducing the "classical" topics and examples fundamental to the discipline. The most important routes to chaos are presented within a unified framework and supported by integrated problem sets. Topics include one- and two-dimensional maps, universality theory, fractal dimension, differential and conservative dynamics, and other subjects. The text is supplemented by a helpful glossary, references, and an index.

Chaos: A Very Short Introduction

Leonard Smith
Chaos A Very Short Introduction Book PDF

Author : Leonard Smith
Publisher : OUP Oxford
Page : 200 pages
File Size : 47,8 Mb
Release : 2007-02-22
Category : Science
ISBN : 9780191579431

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Chaos: A Very Short Introduction by Leonard Smith Pdf

Chaos exists in systems all around us. Even the simplest system of cause and effect can be subject to chaos, denying us accurate predictions of its behaviour, and sometimes giving rise to astonishing structures of large-scale order. Our growing understanding of Chaos Theory is having fascinating applications in the real world - from technology to global warming, politics, human behaviour, and even gambling on the stock market. Leonard Smith shows that we all have an intuitive understanding of chaotic systems. He uses accessible maths and physics (replacing complex equations with simple examples like pendulums, railway lines, and tossing coins) to explain the theory, and points to numerous examples in philosophy and literature (Edgar Allen Poe, Chang-Tzu, Arthur Conan Doyle) that illuminate the problems. The beauty of fractal patterns and their relation to chaos, as well as the history of chaos, and its uses in the real world and implications for the philosophy of science are all discussed in this Very Short Introduction. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

An Introduction To Chaotic Dynamical Systems

Robert Devaney
An Introduction To Chaotic Dynamical Systems Book PDF

Author : Robert Devaney
Publisher : CRC Press
Page : 360 pages
File Size : 44,5 Mb
Release : 2018-03-09
Category : Mathematics
ISBN : 9780429970856

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An Introduction To Chaotic Dynamical Systems by Robert Devaney Pdf

The study of nonlinear dynamical systems has exploded in the past 25 years, and Robert L. Devaney has made these advanced research developments accessible to undergraduate and graduate mathematics students as well as researchers in other disciplines with the introduction of this widely praised book. In this second edition of his best-selling text, Devaney includes new material on the orbit diagram fro maps of the interval and the Mandelbrot set, as well as striking color photos illustrating both Julia and Mandelbrot sets. This book assumes no prior acquaintance with advanced mathematical topics such as measure theory, topology, and differential geometry. Assuming only a knowledge of calculus, Devaney introduces many of the basic concepts of modern dynamical systems theory and leads the reader to the point of current research in several areas.

An Introduction To Chaotic Dynamical Systems

Robert L. Devaney
An Introduction To Chaotic Dynamical Systems Book PDF

Author : Robert L. Devaney
Publisher : CRC Press
Page : 571 pages
File Size : 50,9 Mb
Release : 2021-11-28
Category : Mathematics
ISBN : 9781000486773

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An Introduction To Chaotic Dynamical Systems by Robert L. Devaney Pdf

There is an explosion of interest in dynamical systems in the mathematical community as well as in many areas of science. The results have been truly exciting: systems which once seemed completely intractable from an analytic point of view can now be understood in a geometric or qualitative sense rather easily. Scientists and engineers realize the power and the beauty of the geometric and qualitative techniques. These techniques apply to a number of important nonlinear problems ranging from physics and chemistry to ecology and economics. Computer graphics have allowed us to view the dynamical behavior geometrically. The appearance of incredibly beautiful and intricate objects such as the Mandelbrot set, the Julia set, and other fractals have really piqued interest in the field. This is text is aimed primarily at advanced undergraduate and beginning graduate students. Throughout, the author emphasizes the mathematical aspects of the theory of discrete dynamical systems, not the many and diverse applications of this theory. The field of dynamical systems and especially the study of chaotic systems has been hailed as one of the important breakthroughs in science in the past century and its importance continues to expand. There is no question that the field is becoming more and more important in a variety of scientific disciplines. New to this edition: •Greatly expanded coverage complex dynamics now in Chapter 2 •The third chapter is now devoted to higher dimensional dynamical systems. •Chapters 2 and 3 are independent of one another. •New exercises have been added throughout.

Chaos in Discrete Dynamical Systems

Ralph Abraham,Laura Gardini,Christian Mira
Chaos in Discrete Dynamical Systems Book PDF

Author : Ralph Abraham,Laura Gardini,Christian Mira
Publisher : Springer Science & Business Media
Page : 246 pages
File Size : 55,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781461219361

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Chaos in Discrete Dynamical Systems by Ralph Abraham,Laura Gardini,Christian Mira Pdf

The materials in the book and on the accompanying disc are not solely developed with only the researcher and professional in mind, but also with consideration for the student: most of this material has been class-tested by the authors. The book is packed with some 100 computer graphics to illustrate the material, and the CD-ROM contains full-colour animations tied directly to the subject matter of the book itself. The cross-platform CD also contains the program ENDO, which enables users to create their own 2-D imagery with X-Windows. Maple scripts are provided to allow readers to work directly with the code from which the graphics in the book were taken.

Mathematics for Dynamic Modeling

Edward Beltrami
Mathematics for Dynamic Modeling Book PDF

Author : Edward Beltrami
Publisher : Academic Press
Page : 294 pages
File Size : 46,8 Mb
Release : 2014-05-10
Category : Technology & Engineering
ISBN : 9781483267869

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Mathematics for Dynamic Modeling by Edward Beltrami Pdf

Mathematics for Dynamic Modeling provides an introduction to the mathematics of dynamical systems. This book presents the mathematical formulations in terms of linear and nonlinear differential equations. Organized into two parts encompassing nine chapters, this book begins with an overview of the notions of equilibrium and stability in differential equation modeling that occur in the guise of simple models in the plane. This text then focuses on nonlinear models in which the limiting behavior of orbits can be more complicated. Other chapters consider the problems that illustrate the concepts of equilibrium and stability, limit cycles, chaos, and bifurcation. This book discusses as well a variety of topics, including cusp catastrophes, strange attractors, and reaction–diffusion and shock phenomena. The final chapter deals with models that are based on the notion of optimization. This book is intended to be suitable for students in upper undergraduate and first-year graduate course in mathematical modeling.

Elementary Mathematical Models

Dan Kalman
Elementary Mathematical Models Book PDF

Author : Dan Kalman
Publisher : American Mathematical Society
Page : 363 pages
File Size : 50,8 Mb
Release : 2023-03-09
Category : Mathematics
ISBN : 9781470473006

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Elementary Mathematical Models by Dan Kalman Pdf

The language of mathematics has proven over centuries of application to be an indispensable tool for the expression and analysis of real problems. With numerical, graphical, and theoretical methods, this book examines the relevance of mathematical models to phenomena ranging from population growth and economics to medicine and the physical sciences. In a book written for the intelligent and literate non-mathematician, Kalman aims at an understanding of the power and utility of quantitative methods rather than at technical mastery of mathematical operations. He shows first that mathematical models can serve a critical function in understanding the world, and he concludes with a discussion of the problems encountered by traditional algebraic assumptions in chaos theory. Though models can often approximate future events based on existing data and quantitative relationships, Kalman shows that the appearance of regularity and order can often be misleading. By beginning with quantitative models and ending with an introduction to chaos, Kalman offers a broad treatment of both the power and limitations of quantitatively-based predictions.

Chaotic Dynamics

Tamás Tél,Márton Gruiz
Chaotic Dynamics Book PDF

Author : Tamás Tél,Márton Gruiz
Publisher : Cambridge University Press
Page : 440 pages
File Size : 40,7 Mb
Release : 2006-08-24
Category : Mathematics
ISBN : 0521547830

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Chaotic Dynamics by Tamás Tél,Márton Gruiz Pdf

A clear introduction to chaotic phenomena for undergraduate students in science, engineering, and mathematics.