Ebook: Dynamical Systems with Applications using Maple¿

"The text treats a remarkable spectrum of topics and has a little for everyone. It can serve as an introduction to many of the topics of dynamical systems, and will help even the most jaded reader, such as this reviewer, enjoy some of the interactive aspects of studying dynamics using Maple."

—UK Nonlinear News (Review of First Edition)

"The book will be useful for all kinds of dynamical systems courses…. [It] shows the power of using a computer algebra program to study dynamical systems, and, by giving so many worked examples, provides ample opportunity for experiments. … [It] is well written and a pleasure to read, which is helped by its attention to historical background."

—Mathematical Reviews (Review of First Edition)

Since the first edition of this book was published in 2001, Maple™ has evolved from Maple V into Maple 13. Accordingly, this new edition has been thoroughly updated and expanded to include more applications, examples, and exercises, all with solutions; two new chapters on neural networks and simulation have also been added. There are also new sections on perturbation methods, normal forms, Gröbner bases, and chaos synchronization.

The work provides an introduction to the theory of dynamical systems with the aid of Maple. The author has emphasized breadth of coverage rather than fine detail, and theorems with proof are kept to a minimum. Some of the topics treated are scarcely covered elsewhere. Common themes such as bifurcation, bistability, chaos, instability, multistability, and periodicity run through several chapters.

The book has a hands-on approach, using Maple as a pedagogical tool throughout. Maple worksheet files are listed at the end of each chapter, and along with commands, programs, and output may be viewed in color at the author’s website. Additional applications and further links of interest may be found at Maplesoft’s Application Center.

Dynamical Systems with Applications using Maple is aimed at senior undergraduates, graduate students, and working scientists in various branches of applied mathematics, the natural sciences, and engineering.

ISBN 978-0-8176-4389-8

§

Also by the author:

Dynamical Systems with Applications using MATLAB^®, ISBN 978-0-8176-4321-8

Dynamical Systems with Applications using Mathematica^®, ISBN 978-0-8176-4482-6

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"The text treats a remarkable spectrum of topics and has a little for everyone. It can serve as an introduction to many of the topics of dynamical systems, and will help even the most jaded reader, such as this reviewer, enjoy some of the interactive aspects of studying dynamics using Maple."

—UK Nonlinear News (Review of First Edition)

"The book will be useful for all kinds of dynamical systems courses…. [It] shows the power of using a computer algebra program to study dynamical systems, and, by giving so many worked examples, provides ample opportunity for experiments. … [It] is well written and a pleasure to read, which is helped by its attention to historical background."

—Mathematical Reviews (Review of First Edition)

Since the first edition of this book was published in 2001, Maple™ has evolved from Maple V into Maple 13. Accordingly, this new edition has been thoroughly updated and expanded to include more applications, examples, and exercises, all with solutions; two new chapters on neural networks and simulation have also been added. There are also new sections on perturbation methods, normal forms, Gr?bner bases, and chaos synchronization.

The work provides an introduction to the theory of dynamical systems with the aid of Maple. The author has emphasized breadth of coverage rather than fine detail, and theorems with proof are kept to a minimum. Some of the topics treated are scarcely covered elsewhere. Common themes such as bifurcation, bistability, chaos, instability, multistability, and periodicity run through several chapters.

The book has a hands-on approach, using Maple as a pedagogical tool throughout. Maple worksheet files are listed at the end of each chapter, and along with commands, programs, and output may be viewed in color at the author’s website. Additional applications and further links of interest may be found at Maplesoft’s Application Center.

Dynamical Systems with Applications using Maple is aimed at senior undergraduates, graduate students, and working scientists in various branches of applied mathematics, the natural sciences, and engineering.

ISBN 978-0-8176-4389-8

§

Also by the author:

Dynamical Systems with Applications using MATLAB^®, ISBN 978-0-8176-4321-8

Dynamical Systems with Applications using Mathematica^®, ISBN 978-0-8176-4482-6

---

"The text treats a remarkable spectrum of topics and has a little for everyone. It can serve as an introduction to many of the topics of dynamical systems, and will help even the most jaded reader, such as this reviewer, enjoy some of the interactive aspects of studying dynamics using Maple."

—UK Nonlinear News (Review of First Edition)

"The book will be useful for all kinds of dynamical systems courses…. [It] shows the power of using a computer algebra program to study dynamical systems, and, by giving so many worked examples, provides ample opportunity for experiments. … [It] is well written and a pleasure to read, which is helped by its attention to historical background."

—Mathematical Reviews (Review of First Edition)

Since the first edition of this book was published in 2001, Maple™ has evolved from Maple V into Maple 13. Accordingly, this new edition has been thoroughly updated and expanded to include more applications, examples, and exercises, all with solutions; two new chapters on neural networks and simulation have also been added. There are also new sections on perturbation methods, normal forms, Gr?bner bases, and chaos synchronization.

The work provides an introduction to the theory of dynamical systems with the aid of Maple. The author has emphasized breadth of coverage rather than fine detail, and theorems with proof are kept to a minimum. Some of the topics treated are scarcely covered elsewhere. Common themes such as bifurcation, bistability, chaos, instability, multistability, and periodicity run through several chapters.

The book has a hands-on approach, using Maple as a pedagogical tool throughout. Maple worksheet files are listed at the end of each chapter, and along with commands, programs, and output may be viewed in color at the author’s website. Additional applications and further links of interest may be found at Maplesoft’s Application Center.

Dynamical Systems with Applications using Maple is aimed at senior undergraduates, graduate students, and working scientists in various branches of applied mathematics, the natural sciences, and engineering.

ISBN 978-0-8176-4389-8

§

Also by the author:

Dynamical Systems with Applications using MATLAB^®, ISBN 978-0-8176-4321-8

Dynamical Systems with Applications using Mathematica^®, ISBN 978-0-8176-4482-6

Content:
Front Matter....Pages i-xv
A Tutorial Introduction to Maple....Pages 1-15
Differential Equations....Pages 17-42
Planar Systems....Pages 43-69
Interacting Species....Pages 71-85
Limit Cycles....Pages 87-111
Hamiltonian Systems, Lyapunov Functions, and Stability....Pages 113-127
Bifurcation Theory....Pages 129-145
Three-Dimensional Autonomous Systems and Chaos....Pages 147-171
Poincar? Maps and Nonautonomous Systems in the Plane....Pages 173-196
Local and Global Bifurcations....Pages 197-218
The Second Part of Hilbert’s Sixteenth Problem....Pages 219-241
Linear Discrete Dynamical Systems....Pages 243-261
Nonlinear Discrete Dynamical Systems....Pages 263-295
Complex Iterative Maps....Pages 297-307
Electromagnetic Waves and Optical Resonators....Pages 309-335
Fractals and Multifractals....Pages 337-370
Chaos Control and Synchronization....Pages 371-393
Neural Networks....Pages 395-426
Simulation....Pages 427-444
Examination-Type Questions....Pages 445-451
Back Matter....Pages 1-35
Solutions to Exercises....Pages 453-474

---

"The text treats a remarkable spectrum of topics and has a little for everyone. It can serve as an introduction to many of the topics of dynamical systems, and will help even the most jaded reader, such as this reviewer, enjoy some of the interactive aspects of studying dynamics using Maple."

—UK Nonlinear News (Review of First Edition)

"The book will be useful for all kinds of dynamical systems courses…. [It] shows the power of using a computer algebra program to study dynamical systems, and, by giving so many worked examples, provides ample opportunity for experiments. … [It] is well written and a pleasure to read, which is helped by its attention to historical background."

—Mathematical Reviews (Review of First Edition)

Since the first edition of this book was published in 2001, Maple™ has evolved from Maple V into Maple 13. Accordingly, this new edition has been thoroughly updated and expanded to include more applications, examples, and exercises, all with solutions; two new chapters on neural networks and simulation have also been added. There are also new sections on perturbation methods, normal forms, Gr?bner bases, and chaos synchronization.

The work provides an introduction to the theory of dynamical systems with the aid of Maple. The author has emphasized breadth of coverage rather than fine detail, and theorems with proof are kept to a minimum. Some of the topics treated are scarcely covered elsewhere. Common themes such as bifurcation, bistability, chaos, instability, multistability, and periodicity run through several chapters.

The book has a hands-on approach, using Maple as a pedagogical tool throughout. Maple worksheet files are listed at the end of each chapter, and along with commands, programs, and output may be viewed in color at the author’s website. Additional applications and further links of interest may be found at Maplesoft’s Application Center.

Dynamical Systems with Applications using Maple is aimed at senior undergraduates, graduate students, and working scientists in various branches of applied mathematics, the natural sciences, and engineering.

ISBN 978-0-8176-4389-8

§

Also by the author:

Dynamical Systems with Applications using MATLAB^®, ISBN 978-0-8176-4321-8

Dynamical Systems with Applications using Mathematica^®, ISBN 978-0-8176-4482-6

Content:
Front Matter....Pages i-xv
A Tutorial Introduction to Maple....Pages 1-15
Differential Equations....Pages 17-42
Planar Systems....Pages 43-69
Interacting Species....Pages 71-85
Limit Cycles....Pages 87-111
Hamiltonian Systems, Lyapunov Functions, and Stability....Pages 113-127
Bifurcation Theory....Pages 129-145
Three-Dimensional Autonomous Systems and Chaos....Pages 147-171
Poincar? Maps and Nonautonomous Systems in the Plane....Pages 173-196
Local and Global Bifurcations....Pages 197-218
The Second Part of Hilbert’s Sixteenth Problem....Pages 219-241
Linear Discrete Dynamical Systems....Pages 243-261
Nonlinear Discrete Dynamical Systems....Pages 263-295
Complex Iterative Maps....Pages 297-307
Electromagnetic Waves and Optical Resonators....Pages 309-335
Fractals and Multifractals....Pages 337-370
Chaos Control and Synchronization....Pages 371-393
Neural Networks....Pages 395-426
Simulation....Pages 427-444
Examination-Type Questions....Pages 445-451
Back Matter....Pages 1-35
Solutions to Exercises....Pages 453-474
....