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| > | ![DEplot({DE1}, [N(t), P(t)], t = -2 .. 2, [[N(0) = 1.5, P(0) = .8], [N(0) = 1.5, P(0) = .6], [N(0) = 1.5, P(0) = .4], [N(0) = 1.5, P(0) = .31]], numsteps = 76, title =](videos/MA138_S13_non_linear_24.gif){kind=small} ![DEplot({DE1}, [N(t), P(t)], t = -2 .. 2, [[N(0) = 1.5, P(0) = .8], [N(0) = 1.5, P(0) = .6], [N(0) = 1.5, P(0) = .4], [N(0) = 1.5, P(0) = .31]], numsteps = 76, title =](videos/MA138_S13_non_linear_25.gif){kind=small} ![DEplot({DE1}, [N(t), P(t)], t = -2 .. 2, [[N(0) = 1.5, P(0) = .8], [N(0) = 1.5, P(0) = .6], [N(0) = 1.5, P(0) = .4], [N(0) = 1.5, P(0) = .31]], numsteps = 76, title =](videos/MA138_S13_non_linear_26.gif){kind=small} ![DEplot({DE1}, [N(t), P(t)], t = -2 .. 2, [[N(0) = 1.5, P(0) = .8], [N(0) = 1.5, P(0) = .6], [N(0) = 1.5, P(0) = .4], [N(0) = 1.5, P(0) = .31]], numsteps = 76, title =](videos/MA138_S13_non_linear_27.gif){kind=small} |
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| > | ![DEplot({DE2}, [N(t), P(t)], t = 0 .. 12, [[N(0) = 1.5, P(0) = 1.5], [N(0) = 1.5, P(0) = .6], [N(0) = 3, P(0) = 0.4e-1], [N(0) = 3, P(0) = 1.5]], numsteps = 76, title =](videos/MA138_S13_non_linear_32.gif){kind=small} ![DEplot({DE2}, [N(t), P(t)], t = 0 .. 12, [[N(0) = 1.5, P(0) = 1.5], [N(0) = 1.5, P(0) = .6], [N(0) = 3, P(0) = 0.4e-1], [N(0) = 3, P(0) = 1.5]], numsteps = 76, title =](videos/MA138_S13_non_linear_33.gif){kind=small} ![DEplot({DE2}, [N(t), P(t)], t = 0 .. 12, [[N(0) = 1.5, P(0) = 1.5], [N(0) = 1.5, P(0) = .6], [N(0) = 3, P(0) = 0.4e-1], [N(0) = 3, P(0) = 1.5]], numsteps = 76, title =](videos/MA138_S13_non_linear_34.gif){kind=small} ![DEplot({DE2}, [N(t), P(t)], t = 0 .. 12, [[N(0) = 1.5, P(0) = 1.5], [N(0) = 1.5, P(0) = .6], [N(0) = 3, P(0) = 0.4e-1], [N(0) = 3, P(0) = 1.5]], numsteps = 76, title =](videos/MA138_S13_non_linear_35.gif){kind=small} |
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| > | ![odeplot(sol2, [[t, N(t)], [t, P(t)]], 0 .. 20, linestyle = [1, 3], color = [](videos/MA138_S13_non_linear_41.gif){kind=small} ![odeplot(sol2, [[t, N(t)], [t, P(t)]], 0 .. 20, linestyle = [1, 3], color = [](videos/MA138_S13_non_linear_42.gif){kind=small} |
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| > | ![odeplot(sol2a, [[t, N(t)], [t, P(t)]], 0 .. 20, linestyle = [1, 3], color = [](videos/MA138_S13_non_linear_49.gif){kind=small} ![odeplot(sol2a, [[t, N(t)], [t, P(t)]], 0 .. 20, linestyle = [1, 3], color = [](videos/MA138_S13_non_linear_50.gif){kind=small} |
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(8) |
| > | ![DEplot({DE3}, [x(t), y(t)], t = 0 .. 3, [[x(0) = 2, y(0) = 2], [x(0) = 1.5, y(0) = .6], [x(0) = 2.2, y(0) = 1], [x(0) = 3, y(0) = 1]], numsteps = 76, title =](videos/MA138_S13_non_linear_55.gif){kind=small} ![DEplot({DE3}, [x(t), y(t)], t = 0 .. 3, [[x(0) = 2, y(0) = 2], [x(0) = 1.5, y(0) = .6], [x(0) = 2.2, y(0) = 1], [x(0) = 3, y(0) = 1]], numsteps = 76, title =](videos/MA138_S13_non_linear_56.gif){kind=small} ![DEplot({DE3}, [x(t), y(t)], t = 0 .. 3, [[x(0) = 2, y(0) = 2], [x(0) = 1.5, y(0) = .6], [x(0) = 2.2, y(0) = 1], [x(0) = 3, y(0) = 1]], numsteps = 76, title =](videos/MA138_S13_non_linear_57.gif){kind=small} ![DEplot({DE3}, [x(t), y(t)], t = 0 .. 3, [[x(0) = 2, y(0) = 2], [x(0) = 1.5, y(0) = .6], [x(0) = 2.2, y(0) = 1], [x(0) = 3, y(0) = 1]], numsteps = 76, title =](videos/MA138_S13_non_linear_58.gif){kind=small} |
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| > | ![odeplot(sol3, [[t, x(t)], [t, y(t)]], 0 .. 10, linestyle = [1, 3], color = [](videos/MA138_S13_non_linear_64.gif){kind=small} ![odeplot(sol3, [[t, x(t)], [t, y(t)]], 0 .. 10, linestyle = [1, 3], color = [](videos/MA138_S13_non_linear_65.gif){kind=small} |
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(11) |
| > | ![DEplot({DE4}, [x(t), y(t)], t = 0 .. 15, [[x(0) = .4, y(0) = .4], [x(0) = 1, y(0) = 1], [x(0) = 2, y(0) = .4], [x(0) = .1, y(0) = 1], [x(0) = 0.5e-1, y(0) = .5]], numsteps = 76, title =](videos/MA138_S13_non_linear_70.gif){kind=small} ![DEplot({DE4}, [x(t), y(t)], t = 0 .. 15, [[x(0) = .4, y(0) = .4], [x(0) = 1, y(0) = 1], [x(0) = 2, y(0) = .4], [x(0) = .1, y(0) = 1], [x(0) = 0.5e-1, y(0) = .5]], numsteps = 76, title =](videos/MA138_S13_non_linear_71.gif){kind=small} ![DEplot({DE4}, [x(t), y(t)], t = 0 .. 15, [[x(0) = .4, y(0) = .4], [x(0) = 1, y(0) = 1], [x(0) = 2, y(0) = .4], [x(0) = .1, y(0) = 1], [x(0) = 0.5e-1, y(0) = .5]], numsteps = 76, title =](videos/MA138_S13_non_linear_72.gif){kind=small} ![DEplot({DE4}, [x(t), y(t)], t = 0 .. 15, [[x(0) = .4, y(0) = .4], [x(0) = 1, y(0) = 1], [x(0) = 2, y(0) = .4], [x(0) = .1, y(0) = 1], [x(0) = 0.5e-1, y(0) = .5]], numsteps = 76, title =](videos/MA138_S13_non_linear_73.gif){kind=small} |
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![[implicitplot]](videos/MA138_S13_non_linear_76.gif){kind=small} |
(12) |
| > | implicitplot([x=0, (1-x-y)=0, y=0, (0.75-y-0.5*x)=0], x=-0.5..2.5, y=-0.5..1.5, color=["Blue", "Blue", "Red","Red"], title="Nullclines, DE4"); |
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(13) |
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(14) |
| > | ![odeplot(sol4, [[t, x(t)], [t, y(t)]], 0 .. 20, color = [](videos/MA138_S13_non_linear_82.gif){kind=small} ![odeplot(sol4, [[t, x(t)], [t, y(t)]], 0 .. 20, color = [](videos/MA138_S13_non_linear_83.gif){kind=small} |
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(15) |
| > | ![DEplot({DE5}, [x(t), y(t)], t = 0 .. 15, [[x(0) = .4, y(0) = .4], [x(0) = 1, y(0) = 1], [x(0) = 2, y(0) = .4], [x(0) = .1, y(0) = 1], [x(0) = 0.5e-1, y(0) = .5]], numsteps = 76, title =](videos/MA138_S13_non_linear_88.gif){kind=small} ![DEplot({DE5}, [x(t), y(t)], t = 0 .. 15, [[x(0) = .4, y(0) = .4], [x(0) = 1, y(0) = 1], [x(0) = 2, y(0) = .4], [x(0) = .1, y(0) = 1], [x(0) = 0.5e-1, y(0) = .5]], numsteps = 76, title =](videos/MA138_S13_non_linear_89.gif){kind=small} ![DEplot({DE5}, [x(t), y(t)], t = 0 .. 15, [[x(0) = .4, y(0) = .4], [x(0) = 1, y(0) = 1], [x(0) = 2, y(0) = .4], [x(0) = .1, y(0) = 1], [x(0) = 0.5e-1, y(0) = .5]], numsteps = 76, title =](videos/MA138_S13_non_linear_90.gif){kind=small} ![DEplot({DE5}, [x(t), y(t)], t = 0 .. 15, [[x(0) = .4, y(0) = .4], [x(0) = 1, y(0) = 1], [x(0) = 2, y(0) = .4], [x(0) = .1, y(0) = 1], [x(0) = 0.5e-1, y(0) = .5]], numsteps = 76, title =](videos/MA138_S13_non_linear_91.gif){kind=small} |
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![[implicitplot]](videos/MA138_S13_non_linear_94.gif){kind=small} |
(16) |
| > | implicitplot([x=0, (1-x-y)=0, y=0, (0.5-0.25*y-0.75*x)=0], x=-0.5..2.5, y=-0.5..2.5, color=["Blue", "Blue", "Red","Red"], title="Nullclines, DE5"); |
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| > | ![odeplot(sol5, [[t, x(t)], [t, y(t)]], 0 .. 30, color = [](videos/MA138_S13_non_linear_100.gif){kind=small} ![odeplot(sol5, [[t, x(t)], [t, y(t)]], 0 .. 30, color = [](videos/MA138_S13_non_linear_101.gif){kind=small} |
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(19) |
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(20) |
| > | ![odeplot(sol5e, [[t, x(t)], [t, y(t)]], 0 .. 30, color = [](videos/MA138_S13_non_linear_107.gif){kind=small} ![odeplot(sol5e, [[t, x(t)], [t, y(t)]], 0 .. 30, color = [](videos/MA138_S13_non_linear_108.gif){kind=small} |
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(21) |
| > | ![DEplot({DE6}, [x(t), y(t)], t = 0 .. 15, [[x(0) = .4, y(0) = .4], [x(0) = 1, y(0) = 1], [x(0) = 2, y(0) = .4], [x(0) = .1, y(0) = 1], [x(0) = 0.5e-1, y(0) = .5]], numsteps = 76, title =](videos/MA138_S13_non_linear_112.gif){kind=small} ![DEplot({DE6}, [x(t), y(t)], t = 0 .. 15, [[x(0) = .4, y(0) = .4], [x(0) = 1, y(0) = 1], [x(0) = 2, y(0) = .4], [x(0) = .1, y(0) = 1], [x(0) = 0.5e-1, y(0) = .5]], numsteps = 76, title =](videos/MA138_S13_non_linear_113.gif){kind=small} ![DEplot({DE6}, [x(t), y(t)], t = 0 .. 15, [[x(0) = .4, y(0) = .4], [x(0) = 1, y(0) = 1], [x(0) = 2, y(0) = .4], [x(0) = .1, y(0) = 1], [x(0) = 0.5e-1, y(0) = .5]], numsteps = 76, title =](videos/MA138_S13_non_linear_114.gif){kind=small} ![DEplot({DE6}, [x(t), y(t)], t = 0 .. 15, [[x(0) = .4, y(0) = .4], [x(0) = 1, y(0) = 1], [x(0) = 2, y(0) = .4], [x(0) = .1, y(0) = 1], [x(0) = 0.5e-1, y(0) = .5]], numsteps = 76, title =](videos/MA138_S13_non_linear_115.gif){kind=small} |
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![[implicitplot]](videos/MA138_S13_non_linear_118.gif){kind=small} |
(22) |
| > | implicitplot([x=0, (1-x-y)=0, y=0, (2-y-x)=0], x=-0.5..2.5, y=-0.5..2.5, color=["Blue", "Blue", "Red","Red"], title="Nullclines, DE6"); |
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(23) |
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(24) |
| > | ![odeplot(sol6, [[t, x(t)], [t, y(t)]], 0 .. 30, color = [](videos/MA138_S13_non_linear_124.gif){kind=small} ![odeplot(sol6, [[t, x(t)], [t, y(t)]], 0 .. 30, color = [](videos/MA138_S13_non_linear_125.gif){kind=small} |
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(25) |
| > | ![DEplot({DE7}, [v(t), w(t)], t = 0 .. 70, [[v(0) = .4, w(0) = 0], [v(0) = .2, w(0) = 0], [v(0) = .1, w(0) = -0.5e-1], [v(0) = 1.5, w(0) = 0]], numsteps = 76, title =](videos/MA138_S13_non_linear_131.gif){kind=small} ![DEplot({DE7}, [v(t), w(t)], t = 0 .. 70, [[v(0) = .4, w(0) = 0], [v(0) = .2, w(0) = 0], [v(0) = .1, w(0) = -0.5e-1], [v(0) = 1.5, w(0) = 0]], numsteps = 76, title =](videos/MA138_S13_non_linear_132.gif){kind=small} ![DEplot({DE7}, [v(t), w(t)], t = 0 .. 70, [[v(0) = .4, w(0) = 0], [v(0) = .2, w(0) = 0], [v(0) = .1, w(0) = -0.5e-1], [v(0) = 1.5, w(0) = 0]], numsteps = 76, title =](videos/MA138_S13_non_linear_133.gif){kind=small} ![DEplot({DE7}, [v(t), w(t)], t = 0 .. 70, [[v(0) = .4, w(0) = 0], [v(0) = .2, w(0) = 0], [v(0) = .1, w(0) = -0.5e-1], [v(0) = 1.5, w(0) = 0]], numsteps = 76, title =](videos/MA138_S13_non_linear_134.gif){kind=small} |
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(27) |
| > | ![odeplot(sol7, [[t, v(t)], [t, w(t)]], 0 .. 50, color = [](videos/MA138_S13_non_linear_140.gif){kind=small} ![odeplot(sol7, [[t, v(t)], [t, w(t)]], 0 .. 50, color = [](videos/MA138_S13_non_linear_141.gif){kind=small} |
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(28) |
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(29) |
| > | ![odeplot(sol7e, [[t, v(t)], [t, w(t)]], 0 .. 50, color = [](videos/MA138_S13_non_linear_147.gif){kind=small} ![odeplot(sol7e, [[t, v(t)], [t, w(t)]], 0 .. 50, color = [](videos/MA138_S13_non_linear_148.gif){kind=small} |
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(30) |
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(31) |
| > | ![odeplot(sol7f, [[t, v(t)], [t, w(t)]], 0 .. 100, color = [](videos/MA138_S13_non_linear_155.gif){kind=small} ![odeplot(sol7f, [[t, v(t)], [t, w(t)]], 0 .. 100, color = [](videos/MA138_S13_non_linear_156.gif){kind=small} |
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(32) |
| > | ![DEplot({DE8}, [x(t), y(t)], t = 0 .. 10, [[x(0) = 2, y(0) = 0], [x(0) = 8, y(0) = .6], [x(0) = 3.2, y(0) = .1], [x(0) = 3.1, y(0) = .1], [x(0) = 0, y(0) = 7.5]], numsteps = 76, title =](videos/MA138_S13_non_linear_160.gif){kind=small} ![DEplot({DE8}, [x(t), y(t)], t = 0 .. 10, [[x(0) = 2, y(0) = 0], [x(0) = 8, y(0) = .6], [x(0) = 3.2, y(0) = .1], [x(0) = 3.1, y(0) = .1], [x(0) = 0, y(0) = 7.5]], numsteps = 76, title =](videos/MA138_S13_non_linear_161.gif){kind=small} ![DEplot({DE8}, [x(t), y(t)], t = 0 .. 10, [[x(0) = 2, y(0) = 0], [x(0) = 8, y(0) = .6], [x(0) = 3.2, y(0) = .1], [x(0) = 3.1, y(0) = .1], [x(0) = 0, y(0) = 7.5]], numsteps = 76, title =](videos/MA138_S13_non_linear_162.gif){kind=small} ![DEplot({DE8}, [x(t), y(t)], t = 0 .. 10, [[x(0) = 2, y(0) = 0], [x(0) = 8, y(0) = .6], [x(0) = 3.2, y(0) = .1], [x(0) = 3.1, y(0) = .1], [x(0) = 0, y(0) = 7.5]], numsteps = 76, title =](videos/MA138_S13_non_linear_163.gif){kind=small} ![DEplot({DE8}, [x(t), y(t)], t = 0 .. 10, [[x(0) = 2, y(0) = 0], [x(0) = 8, y(0) = .6], [x(0) = 3.2, y(0) = .1], [x(0) = 3.1, y(0) = .1], [x(0) = 0, y(0) = 7.5]], numsteps = 76, title =](videos/MA138_S13_non_linear_164.gif){kind=small} |
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(33) |
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(34) |
| > | ![odeplot(sol8, [[t, x(t)], [t, y(t)]], 0 .. 30, color = [](videos/MA138_S13_non_linear_170.gif){kind=small} ![odeplot(sol8, [[t, x(t)], [t, y(t)]], 0 .. 30, color = [](videos/MA138_S13_non_linear_171.gif){kind=small} |
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(35) |
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| > | ![DEplot({DE9}, [x(t), y(t)], t = 0 .. 3, [[x(0) = .5, y(0) = .1], [x(0) = 0, y(0) = .3], [x(0) = .2, y(0) = -.2], [x(0) = -.2, y(0) = .2]], numsteps = 76, title =](videos/MA138_S13_non_linear_176.gif){kind=small} ![DEplot({DE9}, [x(t), y(t)], t = 0 .. 3, [[x(0) = .5, y(0) = .1], [x(0) = 0, y(0) = .3], [x(0) = .2, y(0) = -.2], [x(0) = -.2, y(0) = .2]], numsteps = 76, title =](videos/MA138_S13_non_linear_177.gif){kind=small} ![DEplot({DE9}, [x(t), y(t)], t = 0 .. 3, [[x(0) = .5, y(0) = .1], [x(0) = 0, y(0) = .3], [x(0) = .2, y(0) = -.2], [x(0) = -.2, y(0) = .2]], numsteps = 76, title =](videos/MA138_S13_non_linear_178.gif){kind=small} ![DEplot({DE9}, [x(t), y(t)], t = 0 .. 3, [[x(0) = .5, y(0) = .1], [x(0) = 0, y(0) = .3], [x(0) = .2, y(0) = -.2], [x(0) = -.2, y(0) = .2]], numsteps = 76, title =](videos/MA138_S13_non_linear_179.gif){kind=small} |
| Warning, plot may be incomplete, the following errors(s) were issued: |
| cannot evaluate the solution further right of 1.9230790, probably a singularity | |
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(36) |
| > | ![DEplot({DE10}, [x(t), y(t)], t = 0 .. 5, [[x(0) = 0, y(0) = 2], [x(0) = 0, y(0) = -2], [x(0) = 1, y(0) = 0], [x(0) = -1, y(0) = 1]], numsteps = 76, title =](videos/MA138_S13_non_linear_184.gif){kind=small} ![DEplot({DE10}, [x(t), y(t)], t = 0 .. 5, [[x(0) = 0, y(0) = 2], [x(0) = 0, y(0) = -2], [x(0) = 1, y(0) = 0], [x(0) = -1, y(0) = 1]], numsteps = 76, title =](videos/MA138_S13_non_linear_185.gif){kind=small} ![DEplot({DE10}, [x(t), y(t)], t = 0 .. 5, [[x(0) = 0, y(0) = 2], [x(0) = 0, y(0) = -2], [x(0) = 1, y(0) = 0], [x(0) = -1, y(0) = 1]], numsteps = 76, title =](videos/MA138_S13_non_linear_186.gif){kind=small} ![DEplot({DE10}, [x(t), y(t)], t = 0 .. 5, [[x(0) = 0, y(0) = 2], [x(0) = 0, y(0) = -2], [x(0) = 1, y(0) = 0], [x(0) = -1, y(0) = 1]], numsteps = 76, title =](videos/MA138_S13_non_linear_187.gif){kind=small} |
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