Differential Dynamical Systems

This book contains a systematic study of autonomous systems of ordinary differential equations and dynamical systems. It begins with a thorough treatment of linear systems; however, the main topic of the book is local and global behavior of nonlinear systems. The main purpose of the book is to introduce students to the qualitative and geometric theory of ordinary differential equations originated by at the end of the 19th century.

This self-contained book provides systematic instructive analysis of uncertain systems of the following types: ordinary differential equations, impulsive equations, equations on time scales, singularly perturbed differential equations, and set differential equations.

This textbook provides a broad introduction to continuous and discrete dynamical systems. With its hands-on approach, the text leads the reader from basic theory to recently published research material in nonlinear ordinary differential equations, nonlinear optics, multifractals, neural networks, and binary oscillator computing. Dynamical Systems with Applications Using Python takes advantage of Python’s extensive visualization, simulation, and algorithmic tools to study those topics in nonlinear dynamical systems through numerical algorithms and generated diagrams.

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This book brings together important contributions from renowned international researchers to provide an excellent survey of recent advances in dynamical systems theory and applications.

Many textbooks on differential equations are written to be interesting to the teacher rather than the student. Introduction to Differential Equations with Dynamical Systems is directed toward students. This concise and up-to-date textbook addresses the challenges that undergraduate mathematics, engineering, and science students experience during a first course on differential equations.