Solve and plot 3D non-Hyperbolic system

I'm using a method to find asymptotic solutions for the system and I want to check my answer by solving it by Mathematica

Example:

x'[t] == x[t] (x[t]^3 + 2 x[t] y[t] + y[t]^3)

y'[t] == y[t] (x[t]^3 + x[t] y[t] + y[t]^3)

z'[t] == z[t] (x[t]^3 + 2 x[t] y[t] + z[t]^3)

The fixed point here is (0,0,0) I need the plot of the system and see the stability.

Thank you