Differential Dynamical Systems

Differential Dynamical Systems by James D. Meiss presents a comprehensive introduction to both traditional ordinary differential equations and the modern theory of dynamical systems. The text begins by developing the fundamentals of linear systems and matrix algebra before transitioning to non-linear differential equations, with an emphasis on the contraction mapping theorem. This methodical approach lays a firm theoretical foundation for exploring the applications of these concepts across physics, biology, chemistry, and engineering. In later chapters, the book delves into key aspects of dynamical systems theory, discussing topics such as flows, chaos, invariant manifolds, and bifurcation. An appendix offers practical examples through simple codes written in Maple, Mathematica, and MATLAB, enabling readers to implement computational techniques and further understand the dynamic behavior of systems. Aimed at senior undergraduates and first-year graduate students in mathematics, engineering, and the physical sciences, Differential Dynamical Systems assumes a background in differential equations, linear algebra, and advanced calculus. With 412 pages of in-depth analysis and application, this book serves as a valuable resource for those seeking to model and interpret systems characterized by smooth changes.