Practical Numerical Algorithms for Chaotic Systems

This volume has two goals. The first to explain the significant features of chaotic systems in an intuitive yet mathematically sound manner. To this end, the authors rely on mathematics as a language to describe the solutions and properties of systems, but they rarely state theorems and even less often prove them. No prior knowledge of nonlinear system is necessary. The second goal is to present robust, reliable algorithms for simulating nonlinear dynamics. A verbal description of an algorithm often makes complete sense until someone actually sits down to implement it. To avoid this problem, the authors provide detailed pseudocode for each algorithm. Though simulations are a useful tool, simulation data must be interpreted carefully, checked against intuition and theory, and used only for purposes for which it is suited. The authors therefore also present the theoretical underpinnings of the algorithms. Most of the algorithms presented in the book are available in the software package INSITE (Interactive Nonlinear Systems Investigative Toolkit for Everyone). INSITE is a collection of interactive, graphically oriented programs for the simulation and investigation of nonlinear systems with an emphasis on chaotic systems. The software package is distributed separately.