A Dynamical Systems Package Running Under Mathematica
This package contains routines for integrating and plotting solutions of systems of nonlinear ordinary differential equations. The package runs under Mathematica. The Mathematica code in the package is fully documented. There are 21 tutorial notebooks to give you a quick introduction to various features of DynPac. The titles of those tutorials give a brief summary of the scope of the package: Introduction to DynPac; Integration and Plotting (2D); Integration and Plotting (3D); Equilibrium and Stability; Local Solution Near Equilibrium Point; Comparison of Integration Methods; Periodic Solutions of Autonomous Systems; Periodic Solutions of Driven Systems; Orbit Trapping and Index Theory; Phase Portraits; Bifurcation Sequences; Liapunov Functions; Coloring, Dashing and Filling; The Lorenz Equations; Animating the Lorenz Attractor; Graph Labels; Lag Equations; Iterated Maps; A Single First-Order Equation; Transformations of Systems; Choosing a Time Step. A number of sample applications are included in addition to these tutorials.
Submitted April 1, 2019 dynamical systems education Differential Equations ode published