Is it possible for a 3 by 3 matrix to use Trace-Determinants plane to see convergency? I am showing in a report the trace det graph if solutions to different equations for linear systems will convert (attractor) or divert (repulsor). Is it possible to draw a 3D graph showing the correlation between the Trace(A) and Det(A) for a 3 by 3 linear system to show if the system will converge or not, in the same way you would for a 2 by 2 system. 

No, you need to take into account all the coefficients of the characteristic polynomial, not just the trace and the determinant.
For a $3 \times 3$ matrix $A$, with characteristic polynomial
$$
p(\lambda)=\det(\lambda I-A)=\lambda^3 + a_2 \lambda^2 + a_1 \lambda + a_0
$$
(where $a_0=-\det A$ and $a_2=-\operatorname{tr} A$),
all eigenvalues have negative real part if and only if $a_0>0$, $a_2>0$ and $a_2 a_1>a_0$, according to the
Routh–Hurwitz criterion.
