Parametric plot from the results of NDSolve

I'm having a bit of trouble making a ParametricPlot from two curves, At fisrt I was having difficulty solving my systems of autonomous ODEs, but then finally got a way to solve it. However, I am now not able to figure out how to get the parametric plot.

solution[t_] =
With[{n = 1.5},
NDSolve[
{q'[t] ==
((q[t]^2)/3)*(3 - n)*x[t]^2 - ((q[t]^2)/3)*n*(y[t] - 1) - ((q[t]^2)/3) + (q[t]*x[t]/3)*(3 - n)*x[t]^2 - (q[t]*x[t]/3)*n*(y[t] - 1) + (q[t]*x[t]/3) + (1/3)*x[t]^2 - (1/3) + (1/3)*((n*y[t]/(n - 1))),
y'[t] ==
((2*y[t]*x[t]^2)/3)*(3 - n)*(x[t] + q[t]) + (2*x[t]*y[t]/3)*((n^2 - 2*n + 2)/(n - 1)) - (2*x[t]*y[t]/3)*n*y[t] + (2*q[t]*n*y[t]*((1 - y[t])/3)),
x'[t] ==
((x[t]^3)/3)*(3 - n)*(q[t] + x[t]) + ((x[t]^2)/3)*n*(2 - y[t]) - 5*((x[t]^2)/3) + (q[t]*x[t]/3)* n*(1 - y[t]) - (q[t]*x[t]) + (1/3)*((n*(n - 2)*y[t])/(n - 1)) - (1/3)*n + 2/3,
q == -1.33, y == 0.88, x == 0.33},
{q[t], y[t],  x[t]}, {t, 0, 10}]][[1, All, 2]]

Plot[solution[t], {t, 0, 10}]

I want to get a parametric plot of q[t] and y[t]. And eventually a 3D plot of q[t], y[t], x[t].

The issue you are facing is to correctly call out the desired dependent variables. So, you need to specify the position of the output. For example, you want to have q[x] then you need to use solution[t][].

For parametric plot, try this out,

ParametricPlot[{solution[t][], solution[t][]}, {t, 0, 10}]

and then for 3D

ParametricPlot3D[{solution[t][], solution[t][], solution[t][]}, {t, 0, 10}]

Redefine your solution a little bit to

solution :=
With[{n = 1.5},
NDSolve[{q'[t] == ((q[t]^2)/3)*(3 - n)*x[t]^2 - ((q[t]^2)/3)*
n*(y[t] - 1) - ((q[t]^2)/3) + (q[t]*x[t]/3)*(3 - n)*
x[t]^2 - (q[t]*x[t]/3)*n*(y[t] - 1) + (q[t]*x[t]/3) + (1/3)*
x[t]^2 - (1/3) + (1/3)*((n*y[t]/(n - 1))),
y'[t] == ((2*y[t]*x[t]^2)/3)*(3 - n)*(x[t] + q[t]) + (2*x[t]*
y[t]/3)*((n^2 - 2*n + 2)/(n - 1)) - (2*x[t]*y[t]/3)*n*
y[t] + (2*q[t]*n*y[t]*((1 - y[t])/3)),
x'[t] == ((x[t]^3)/3)*(3 - n)*(q[t] + x[t]) + ((x[t]^2)/3)*
n*(2 - y[t]) -
5*((x[t]^2)/3) + (q[t]*x[t]/3)*
n*(1 - y[t]) - (q[t]*
x[t]) + (1/3)*((n*(n - 2)*y[t])/(n - 1)) - (1/3)*n + 2/3,
q == -1.33, y == 0.88, x == 0.33}, {q , y , x }, {t, 0,
10}]] []

Now you can plot your results

Plot[Evaluate[ {q[t], y[t]} /. solution ], {t, 0, 10}] • Thank you so much for the assist! – Logan Jacobs Oct 10 '18 at 9:51