Manipulate[
ParametricPlot3D[
Evaluate[{x[t],y[t],z[t]}/.
Quiet@NDSolve[
{x'[t]k1*A*y[t]-k2*x[t]*y[t]+k5*A*x[t]-2k6*x[t]^2,
y'[t]-k1*A*y[t]-k2*x[t]y[t]+f*k7*z[t],
z'[t]k5*A*x[t]-k7*z[t],x[0]x0,y[0]y0,z[0]z0},{x[t],y[t],z[t]},{t,0,tmax}]],
{t,0,tmax},
AxesLabel{"X","Y","Z"},PlotRange{{0,5},{0,5},{0,10}}],
{{tmax,60,"t"},.1,100,Appearance"Labeled"},
{{x0,.25,"x0"},0,1,0.1,Appearance"Labeled"},
{{y0,1,"y0"},0,1,0.1,Appearance"Labeled"},
{{z0,.83,"z0"},0,1,0.1,Appearance"Labeled"},
{{A,1,"A"},0,1,0.1,Appearance"Labeled"},
{{f,1,"f"},0,1,0.1,Appearance"Labeled"},
{{k1,.1,"k1"},0,2,.01,Appearance"Labeled"},
{{k2,1.8,"k2"},0,2,.01,Appearance"Labeled"},
{{k5,2,"k5"},0,2,.01,Appearance"Labeled"},
{{k6,.2,"k6"},0,2,.01,Appearance"Labeled"},
{{k7,.4,"k7"},0,2,.01,Appearance"Labeled"}
]
