Clear[Q,  P,  ode1, ode2]

d = 0.5;
f = 0.75;
g = 0.25;
	
	ode1 =  P'[t] == P[t] (1.  - d Q[t])
ode2 =  Q'[t]  == Q[t] (- f +  g  P[t])


sol = 
        NDSolve[{ode1,  ode2,  P[0. ] == 1.0,  Q[0. ] == 1.0},  {P[t], 
            Q[t]},  {t, 0, 20}];

\(
\(\(p1 = 
      Plot[Evaluate[{P[t]} /. sol], \ {t, 0, 
          20}, 
		PlotRange -> {0, 10}, \ 
        PlotStyle -> {RGBColor[1, 0, 
              0]}, 
		PlotLabel -> "P1 Population size"]\)\(
\)\(
\)
    \)\)
\(p2 = 
      Plot[Evaluate[{Q[t]} /. sol], \ {t, 0, 
          20}, 
		PlotRange -> {0, 10}, \ 
        PlotStyle -> {RGBColor[1, 0, 
              0]}, 
		PlotLabel -> "P2 Population size"]\)

Show[p1, p2]

q3 = P[t] /. sol[[1]]
q4 = Q[t] /. sol[[1]]
phaseplot2 = ParametricPlot[{q3, q4}, {t, 0, 20}]

A = {{2, 1, 3}, {0, 1, 1},  {0, 1, -1}}

MatrixForm[A]
Eigenvalues[A]
Eigenvectors[A]