I’ll use the Lotka-Volterra model as an example since I can’t copy your code.

First way:

Use `Show`

to get the forward `t>0`

and backward `t<0`

solutions to be different colors.

```
{xsol, ysol} = NDSolveValue({
x'(t) == x(t) - 2 x(t) y(t),
y'(t) == x(t) y(t) - y(t),
x(0) == y(0) == 1},
{x, y}, {t, -20, 20})
Show({
ParametricPlot({xsol(t), ysol(t)}, {t, -4, 0}, PlotStyle -> Red,
PlotRange -> {{0, 2.5}, {0, 1.5}},
Prolog -> {PointSize(Large), Blue, Point({1, 1})}),
ParametricPlot({xsol(t), ysol(t)}, {t, 0, 4}, PlotStyle -> Green)})
```

Second way:

Have a forward and a backward `NDSolve`

.

Forward solution

```
{xsolf, ysolf} = NDSolveValue({
x'(t) == x(t) - 2 x(t) y(t),
y'(t) == x(t) y(t) - y(t),
x(0) == y(0) == 1},
{x, y}, {t, 0, 20})
```

Backward solution

```
{xsolb, ysolb} = NDSolveValue({
x'(t) == -(x(t) - 2 x(t) y(t)),
y'(t) == -(x(t) y(t) - y(t)),
x(0) == y(0) == 1},
{x, y}, {t, 0, 20})
```

Notice that the backward solve has the same initial conditions and time range as the forward solve, but that the equations are negated.

This lets you use only a single `ParametricPlot`

for both forward and backward solutions.

```
ParametricPlot({{xsolf(t), ysolf(t)}, {xsolb(t), ysolb(t)}}, {t, 0, 4},
PlotStyle -> {Red, Green},
Prolog -> {PointSize(Large), Blue, Point({1, 1})})
```

I’ve also gone with `NDSolveValue`

instead of the regular `NDSolve`

since you asked to store the data in a table which you can do pretty easily with

```
xfData = Table(xsolf(t), {t, 0, 5, .1})
```

If you use the second way, remember that for the backward solve time is “negative time” so you might need to do something like

```
xbData = Table(xsolb(t), {t, 10, 0, -.1})
```