Dynamical Systems with Applications using MAPLE

by Stephen Lynch

0 A Tutorial Introduction to Maple.- 1 Differential Equations.- 2 Linear Systems in the Plane.- 3 Nonlinear Systems in the Plane.- 4 Interacting Species.- 5 Limit Cycles.- 6 Hamiltonian Systems, Lyapunov Functions, and Stability.- 7 Bifurcation Theory.- 8 Three-Dimensional Autonomous Systems and Chaos.- 9 Poincaré Maps and Nonautonomous Systems in the Plane.- 10 Local and Global Bifurcations.- 11 The Second Part of David Hilbert's Sixteenth Problem.- 12 Limit Cycles of Liénard Systems.- 13 Linear Discrete Dynamical Systems.- 14 Nonlinear Discrete Dynamical Systems.- 15 Complex Iterative Maps.- 16 Electromagnetic Waves and Optical Resonators.- 17 Analysis of Nonlinear Optical Resonators.- 18 Fractals.- 19 Multifractals.- 20 Controlling Chaos.- 21 Examination-Type Questions.- 22 Solutions to Exercises.- References.- Textbooks.- Research Papers.

418 pages, Paperback

First published December 29, 2000