Introduction To Mathematical Modeling Using Discrete Dynamical Systems
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Introduction To Mathematical Modeling Using Discrete Dynamical Systems
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Author : Frederick R. Marotto
language : en
Publisher: Cengage Learning
Release Date : 2005-09-01
Introduction To Mathematical Modeling Using Discrete Dynamical Systems written by Frederick R. Marotto and has been published by Cengage Learning this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-09-01 with Discrete-time systems categories.
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.
Introduction To Mathematical Modeling And Chaotic Dynamics
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Author : Ranjit Kumar Upadhyay
language : en
Publisher: CRC Press
Release Date : 2013-07-23
Introduction To Mathematical Modeling And Chaotic Dynamics written by Ranjit Kumar Upadhyay and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-23 with Mathematics categories.
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.
Discrete Dynamical Models
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Author : Ernesto Salinelli
language : en
Publisher: Springer
Release Date : 2014-06-11
Discrete Dynamical Models written by Ernesto Salinelli and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-11 with Mathematics categories.
This book provides an introduction to the analysis of discrete dynamical systems. The content is presented by an unitary approach that blends the perspective of mathematical modeling together with the ones of several discipline as Mathematical Analysis, Linear Algebra, Numerical Analysis, Systems Theory and Probability. After a preliminary discussion of several models, the main tools for the study of linear and non-linear scalar dynamical systems are presented, paying particular attention to the stability analysis. Linear difference equations are studied in detail and an elementary introduction of Z and Discrete Fourier Transform is presented. A whole chapter is devoted to the study of bifurcations and chaotic dynamics. One-step vector-valued dynamical systems are the subject of three chapters, where the reader can find the applications to positive systems, Markov chains, networks and search engines. The book is addressed mainly to students in Mathematics, Engineering, Physics, Chemistry, Biology and Economics. The exposition is self-contained: some appendices present prerequisites, algorithms and suggestions for computer simulations. The analysis of several examples is enriched by the proposition of many related exercises of increasing difficulty; in the last chapter the detailed solution is given for most of them.
Discrete Dynamical Modeling
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Author : James T. Sandefur
language : en
Publisher: Oxford University Press, USA
Release Date : 1993
Discrete Dynamical Modeling written by James T. Sandefur and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
An introduction to a wide range of techniques and applications used in dynamical mathematical modelling. Emphasizing algebraic concepts, the text encourages students to develop a different manner of thinking about mathematics in order to apply mathematical concepts to other fields.
Analysis And Modelling Of Discrete Dynamical Systems
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Author : Daniel Benest
language : en
Publisher: CRC Press
Release Date : 1998-10-28
Analysis And Modelling Of Discrete Dynamical Systems written by Daniel Benest and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-10-28 with Computers categories.
The theory of dynamical systems, or mappings, plays an important role in various disciplines of modern physics, including celestial mechanics and fluid mechanics. This comprehensive introduction to the general study of mappings has particular emphasis on their applications to the dynamics of the solar system. The book forms a bridge between continuous systems, which are suited to analytical developments and to discrete systems, which are suitable for numerical exploration. Featuring chapters based on lectures delivered at the School on Discrete Dynamical Systems (Aussois, France, February 1996) the book contains three parts - Numerical Tools and Modelling, Analytical Methods, and Examples of Application. It provides a single source of information that, until now, has been available only in widely dispersed journal articles.
Modeling Identification And Simulation Of Dynamical Systems
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Author : P. P. J. van den Bosch
language : en
Publisher: CRC Press
Release Date : 2020-12-17
Modeling Identification And Simulation Of Dynamical Systems written by P. P. J. van den Bosch and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-17 with Mathematics categories.
This book gives an in-depth introduction to the areas of modeling, identification, simulation, and optimization. These scientific topics play an increasingly dominant part in many engineering areas such as electrotechnology, mechanical engineering, aerospace, and physics. This book represents a unique and concise treatment of the mutual interactions among these topics. Techniques for solving general nonlinear optimization problems as they arise in identification and many synthesis and design methods are detailed. The main points in deriving mathematical models via prior knowledge concerning the physics describing a system are emphasized. Several chapters discuss the identification of black-box models. Simulation is introduced as a numerical tool for calculating time responses of almost any mathematical model. The last chapter covers optimization, a generally applicable tool for formulating and solving many engineering problems.
Discrete Dynamical Systems And Difference Equations With Mathematica
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Author : Mustafa R.S. Kulenovic
language : en
Publisher: CRC Press
Release Date : 2002-02-27
Discrete Dynamical Systems And Difference Equations With Mathematica written by Mustafa R.S. Kulenovic and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-02-27 with Mathematics categories.
Following the work of Yorke and Li in 1975, the theory of discrete dynamical systems and difference equations developed rapidly. The applications of difference equations also grew rapidly, especially with the introduction of graphical-interface software that can plot trajectories, calculate Lyapunov exponents, plot bifurcation diagrams, and find ba
Dynamical Systems With Applications Using Matlab
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Author : Stephen Lynch
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Dynamical Systems With Applications Using Matlab written by Stephen Lynch 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 2013-12-01 with Technology & Engineering categories.
This introduction to dynamical systems theory guides readers through theory via example and the graphical MATLAB interface; the SIMULINK® accessory is used to simulate real-world dynamical processes. Examples included are from mechanics, electrical circuits, economics, population dynamics, epidemiology, nonlinear optics, materials science and neural networks. The book contains over 330 illustrations, 300 examples, and exercises with solutions.
Mathematical Modelling
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Author : Seyed M. Moghadas
language : en
Publisher: John Wiley & Sons
Release Date : 2018-08-28
Mathematical Modelling written by Seyed M. Moghadas and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-28 with Mathematics categories.
An important resource that provides an overview of mathematical modelling Mathematical Modelling offers a comprehensive guide to both analytical and computational aspects of mathematical modelling that encompasses a wide range of subjects. The authors provide an overview of the basic concepts of mathematical modelling and review the relevant topics from differential equations and linear algebra. The text explores the various types of mathematical models, and includes a range of examples that help to describe a variety of techniques from dynamical systems theory. The book’s analytical techniques examine compartmental modelling, stability, bifurcation, discretization, and fixed-point analysis. The theoretical analyses involve systems of ordinary differential equations for deterministic models. The text also contains information on concepts of probability and random variables as the requirements of stochastic processes. In addition, the authors describe algorithms for computer simulation of both deterministic and stochastic models, and review a number of well-known models that illustrate their application in different fields of study. This important resource: Includes a broad spectrum of models that fall under deterministic and stochastic classes and discusses them in both continuous and discrete forms Demonstrates the wide spectrum of problems that can be addressed through mathematical modelling based on fundamental tools and techniques in applied mathematics and statistics Contains an appendix that reveals the overall approach that can be taken to solve exercises in different chapters Offers many exercises to help better understand the modelling process Written for graduate students in applied mathematics, instructors, and professionals using mathematical modelling for research and training purposes, Mathematical Modelling: A Graduate Textbook covers a broad range of analytical and computational aspects of mathematical modelling.
Discrete Dynamical Systems
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Author : James T. Sandefur
language : en
Publisher:
Release Date : 1990
Discrete Dynamical Systems written by James T. Sandefur and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Chaos categories.
Discrete dynamics is the study of change. In particular, it shows how to translate real world situations into the language of mathematics. With the increase in computational ability and the recent interest in chaos, discrete dynamics has emerged as an important area of mathematical study. This text is the first to provide an elementary introduction to the world of dynamical systems. The aim of the text is to explain both the wide variety of techniques used to study dynamical systems and their many applications in areas ranging from population growth to problems in genetics. This investigation leads to the fruitful concepts of stability, strange attractors, chaos, and fractals. Very little previous mathematical knowledge is assumed and students with an elementary exposure to calculus and linear algebra will be able to follow the text easily. A large number of worked examples and exercises are provided to assist instruction. Throughout, students are encouraged to experiment with models of dynamical systems on computers and explore this fascinating area of mathematics on their own.