This Maple file shows three animations. The first is a nonlinear, undamped pendulum. The second is a competing species model, and the third is a predator-prey model. If you want to have all of them get constructed, press the button above with three exclamation points: !!! To play the animation, click on the plot and a play button will show up under the toolbars above. Eqn1:=diff(x(t),t)=y(t), diff(y(t),t)=-sin(x(t)); with(DEtools): DEplot({Eqn1},{x(t),y(t)},t=0..8,x=-10..10,y=-3..3,arrows = comet, animatefield = true, numframes = 50, dirfield = 300); PkkkTFZTRzYiNyQvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInhHRiQ2I0kidEdGJEYuKiZGKyIiIiwoRjBGMEYrISIiLUkieUdGJEYtRjJGMC8tRig2JEYzRi4qJkYzRjAsKEYrJCEjdiEiIyQiIiZGMkYwRjMkISNERjxGMA== JSFH LUknREVwbG90RzYiNitJJExWU0dGJDckLUkieEdGJDYjSSJ0R0YkLUkieUdGJEYqL0YrOyIiISIjNy9GKTshIiIiIiQvRi1GMy9JJ2Fycm93c0dGJEkmY29tZXRHRiQvSS1hbmltYXRlZmllbGRHRiRJJXRydWVHJSpwcm90ZWN0ZWRHL0kqbnVtZnJhbWVzR0YkIiNdL0kpZGlyZmllbGRHRiQiJCsk PkkkTFZTRzYiNyQvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInhHRiQ2I0kidEdGJEYuKiZGKyIiIiwmRjBGMC1JInlHRiRGLSQhIiYhIiJGMC8tRig2JEYyRi4qJkYyRjAsJkYrJCIjRCEiIyQhI3ZGPkYwRjA= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUknREVwbG90RzYiNitJJExWU0dGJDckLUkieEdGJDYjSSJ0R0YkLUkieUdGJEYqL0YrOyIiISIjNy9GKTtGMCIjNS9GLTtGMCIiJi9JJ2Fycm93c0dGJEkmY29tZXRHRiQvSS1hbmltYXRlZmllbGRHRiRJJXRydWVHJSpwcm90ZWN0ZWRHL0kqbnVtZnJhbWVzR0YkIiNdL0kpZGlyZmllbGRHRiQiJCsk