Visualize Chaos in a Delay Differential Equation 

Study the onset of chaos in a dynamical system governed by a delay differential equation.

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X sol = DSolve[{x'[t] == Sign[x[t - 2]] - x[t - 2], x[t /; t <= 0] == 1/10}, x, {t, 0, 25}];

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In[2]:=

X Grid[{{Plot[x[t] /. sol, {t, 0, 25}, ImageSize -> 225, PlotLabel -> Row[{x[t], " vs. ", t}], AspectRatio -> 1], ParametricPlot[Evaluate[{x[t - 2], x[t]} /. sol], {t, 2, 25}, ImageSize -> 225, PlotLabel -> Row[{x[t], " vs. ", x[t - 2]}]]}}]

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