This book was mostly written by a machine that was programmed to search a system of equations for chaotic solutions, simplify the equations to the extent possible, analyze the behavior, produce figures, and write the accompanying text. The equations are coupled autonomous ordinary differential equations with three variables and at least one nonlinearity. Fifty simple systems are included. Some are old and familiar; others are relatively new and unknown. They are chosen to illustrate by simple example most of dynamical behaviors that can occur in low-dimensional chaotic systems.

There is no substitute for the thrill and insight of seeing the solution of a simple equation unfold as the trajectory wanders in real time across your computer screen using a program of your own making. A goal of this book is to inspire and delight as well as to teach. It provides a wealth of examples ripe for further study and extension, and it offers a glimpse of a future when artificial intelligence supplants many of the mundane tasks that accompany dynamical systems research and becomes a true and tireless collaborator.

Contents:

• Preface


• Introduction


• JCS-08-13-2022 System


• Lorenz System


• Rössler System


• Nosé–Hoover System


• Diffusionless Lorenz System


• Sprott C System


• Sprott D System


• Sprott E System


• Sprott F System


• Sprott G System


• Sprott H System


• Sprott I System


• Sprott J System


• Sprott K System


• Sprott L System


• Sprott M System


• Sprott N System


• Sprott O System


• Sprott P System


• Sprott Q System


• Sprott R System


• Sprott S System


• Rössler Prototype-4 System


• Simplest Chaotic System


• Malasoma System


• Moore–Spiegel System


• Linz–Sprott System


• Elwakil–Kennedy System


• Chua System


• Chen System


• Halvorsen System


• Thomas System


• Rabinovich–Fabrikant System


• Leipnik–Newton System


• Arnéodo–Coullet–Tresser System


• Lorenz-84 System


• Wei System


• Wang–Chen System


• Reflection Symmetric System


• Butterfly System


• Line Equilibrium System


• Mostly Quadratic System


• Dissipative–Conservative System


• Time-Reversible Reflection-Invariant System


• Plane Equilibrium System


• Forced Ueda System


• Megastable System


• Attracting Torus System


• Buncha System


• Signum Thermostat System


• Bibliography


• Index


• About the Author

Readership: Advanced undergraduates, graduate students and researchers studying chaotic systems, as well as educators.