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

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