## Abstract

This program draws three-dimensional graphs and relevant planar graphs for either of the following:

- An
*autonomous*system of differential equations of the formIn this case the trajectories are drawn in$$ \frac{{dx}} {{dt}} = f(x,y,z),{\text{ }}\frac{{dy}} {{dt}} = g(x,y,z),{\text{ }}and{\text{ }}\frac{{dz}} {{dt}} = h(x,y,z). $$*xyz*-space and the planar views are*xy*,*xz*,*yz*. The program also locates and analyzes singularities in*xyz*-space. (Three more planar views:*xt*,*yt*, and*zt*are not visible on the screen, but you can ask for the printouts to show them.) - A
*nonautonomous*system of differential equations of the formHere the trajectories are drawn in txy-space and the planar views are$$ \frac{{dx}} {{dt}} = f(t,x,y),{\text{ and }}\frac{{dy}} {{dt}} = g(t,x,y). $$*xy*,*tx*,*ty*. In this case the program does not locate and analyze singularities since it is setting*z*=*t*(hence*dz/dt*= 1 and there can be no 3D singularities). However it allows you the choice of investigating Poincaré sections provided the nonautonomous 2D differential equations are periodic in*t*. This will be explained at the end of this section.

### Keywords

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## Copyright information

© Springer-Verlag New York, Inc. 1993