In[]:=
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"}​​]
Out[]=
​
t
61.3
x0
0.5
y0
0.6
z0
0.4
A
1
f
0.8
k1
0.19
k2
1.98
k5
1.8
k6
0.26
k7
0.3