Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering

The goal of this Third Edition is the same as previous editions: to provide a good foundation - and a joyful experience! - for anyone who'd like to learn about nonlinear dynamics and chaos from an applied perspective.

The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, strange attractors, and synchronization.

The prerequisites are comfort with multivariable calculus and linear algebra, as well as a first course in physics.

Changes to this edition include substantial exercises about conceptual models of climate change, an updated treatment of the SIR model of epidemics, and amendments (based on recent research) about the Selkov model of oscillatory glycolysis. Equations, diagrams, and explanations have been reconsidered and often revised. There are also about 50 new references, many from the recent literature.

The most notable change is a new chapter about the Kuramoto model.

This icon of nonlinear dynamics, introduced in 1975 by the Japanese physicist Yoshiki Kuramoto, is one of the rare examples of a high-dimensional nonlinear system that can be solved by elementary means. It provides an entre to current research on complex systems, synchronization, and networks, yet is accessible to newcomers.

Students and teachers have embraced the book in the past for its exceptional clarity and rich applications, and its general approach and framework continue to be sound.