Elements of Applied Bifurcation Theory

This book focuses on efficient numerical implementations of dynamical systems theory for advanced undergraduates, graduates, Ph.D. students, and researchers in applied mathematics, physics, biology, engineering, and economics. It assumes a moderate mathematical background and incorporates recent theoretical developments, including new and improved numerical methods for bifurcation analysis.

Format: Hardback
Length: 703 pages
Publication date: 19 April 2023
Publisher: Springer International Publishing AG

Providing readers with a solid basis in dynamical systems theory, as well as explicit procedures for applying general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the first while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis.

Dynamical systems theory is a fundamental branch of mathematics that deals with the study of systems that change over time. It encompasses a wide range of topics, including oscillators, differential equations, and complex systems. One of the key challenges in dynamical systems theory is the development of efficient numerical methods for solving these systems. This book aims to provide readers with a solid foundation in dynamical systems theory, as well as explicit procedures for applying general mathematical results to particular problems.

The focus of the book is on efficient numerical implementations of the developed techniques. It begins by introducing the basic concepts of dynamical systems theory, including stability, bifurcations, and chaos. It then discusses the numerical methods used to solve these systems, including finite difference methods, finite element methods, and Monte Carlo methods. The book also includes examples of applications of dynamical systems theory in various fields, such as physics, biology, engineering, and economics.

One of the key features of the book is its emphasis on practical implementation. It provides readers with detailed instructions on how to implement the numerical methods discussed in the book, including the necessary software and programming languages. This makes the book accessible to a wide range of readers, including those with limited mathematical backgrounds.

Another important feature of the book is its emphasis on recent theoretical developments. It incorporates recent advances in numerical methods for bifurcation analysis, which is a critical tool in dynamical systems theory. Bifurcation analysis is used to study the behavior of systems as they approach critical points, where sudden changes in behavior occur. By understanding the behavior of these systems, researchers can develop new models and predict the behavior of complex systems.

The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This makes the book accessible to a wide range of readers, including those with limited mathematical backgrounds.

In conclusion, this book provides readers with a solid foundation in dynamical systems theory, as well as explicit procedures for applying general mathematical results to particular problems. It emphasizes efficient numerical implementations of the developed techniques and includes examples of applications in various fields. The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies.

Weight: 1256g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031220067
Edition number: 4th ed. 2023