Clear[Field, x, y]; Field[x_, y_] = {-0.036 x E^x^2 + 0.123 y, 0.123 x - 0.087 y E^y^2}; fieldplot = Table[Vector[Field[x, y]/(1 + Norm[Field[x, y]]), Tail -> {x, y}], {x, -1.25, 1.25, 2.5/10}, {y, -1.25, 1.25, 2.5/10}]; Clear[x, y, t, solns]; endtime = 100; solns = ParametricNDSolve[{ x'[t] == -0.036 x[t] E^x[t]^2 + 0.123 y[t], y'[t] == 0.123 x[t] - 0.087 y[t] E^y[t]^2, x[0] == a, y[0] == b}, {x, y}, {t, 0, endtime}, {a, b}] Manipulate[ Show[fieldplot, ParametricPlot[{x[t] /. solns[[1]], y[t] /. solns[[1]]}, {t, 0, endtime}, PlotStyle -> {{Red, Thickness[0.015]}}], Graphics[{Red, PointSize[0.06], Point[{a, b}]}], Axes -> True, AxesLabel -> {"x", "y"}, PlotRange -> All], {{a, -1, "x-start"}, -1, 1, Appearance -> "Labeled"}, {{b, -1, "y-start"}, -1, 1, Appearance -> "Labeled"}] I am trying to use manipulate to change the values of a and b in my “solns” equation, and then use those values as initial conditions to the differential equation that I am solving. However, the curve does not appear when I try plotting my function.
How can I have the manipulate function update the variables a and b in my “solns” equation, and then plot that differential equation?
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