Dynamical Systems with Applications using MATLAB provides a comprehensive introduction to the theory of dynamical systems and is designed for use by both advanced undergraduate and beginning graduate students. Its vast compilation of applications also makes this text a great resource for applied mathematicians, engineers, physicists, and researchers in economics, scientific computing, chemistry, biology, population dynamics, neural networks, nonlinear optics, and more. Using a hands-on approach, the author develops the material in a way that will be accessible to a wide range of readers of varying mathematical background. Mathematical theory is presented succinctly to avoid overwhelming the reader with extraneous definitions, theorems, and proofs; the author is careful, however, to include fundamental theorems such as the Existence and Uniqueness of Solutions Theorem, the Hartman-Grobman Theorem, the Center Manifold Theorem, and the Poincaré-Bendixson Theorem. For efficacious use of the text, knowledge of computer programing is necessary and MATLAB proficiency is advantageous. It is additionally recommended that readers complete the following undergraduate courses prior to use: the calculus sequence, linear algebra, real and complex analysis, and ordinary differential equations.
Chapter one provides a tutorial introduction to MATLAB entailing the program basics, the symbolic math toolbox, plotting, differential equations, and the use of program files. While instructive, the MATLAB tutorial is supplemental. The author acknowledges that the included content acts only as a summary of the featured command types, but his assertion that MATLAB novices can utilize the embedded guide to gain familiarity with MATLAB in a few hours does seem to understate the amount of time reasonably required. Undergraduate instructors employing this work as their primary text should consider mandating a scientific computing course as prerequisite or plan to devote time at the beginning of their own course explicitly to MATLAB instruction. Degree programs using MATLAB from calculus on would benefit from not having any start up costs in using this book.
The following chapters define and develop the theory of discrete and continuous dynamical systems using essential theoretical and computational methods. The study of continuous systems is done using the framework of ordinary differential equations. Other continuous systems such as partial differential equations, stochastic systems, and delay differential equations are not covered in this text, but readers are directed to relevant resources in the preface. Throughout these chapters, mathematically interesting topics such as fractals, the Mandelbrot Set, chaos, and brain-inspired computing provide exciting mathematics and beautiful figures while numerous applications illustrate real-world use of the mathematical theory.
The text affords useful resources for both instructors and students, and its formatting is particularly well suited for the former’s use. Instructors will be pleased to find an aims and objectives section at the beginning of each chapter where the author outlines its content and provides student learning objectives. References are listed at the end of each chapter and readers may follow these for more background material and details not provided in the text. Many of the MATLAB program files employed to simulate systems and create the described figures are given at the end of each chapter and are freely available online. This provides a starting point for teachers and students to explore parameters for the given systems and to begin simulating their own systems. In addition, three MATLAB-based examinations are provided as well as answers to all of the book’s exercises.
Stanley R. Huddy is currently a lecturer at the State University of New York at New Paltz. He earned his PhD at Clarkson University under the guidance of Joseph D. Skufca in 2013. His current interests are dynamic behaviors and synchronization patterns on networks of nonlinear systems as well as their applications, delay differential equations, inverse problems, and game theory.