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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"}​
​]
 
 
 
​
t
54.8
 
 
 
x0
0.25
 
 
 
y0
1
 
 
 
z0
0.83
 
 
 
A
1
 
 
 
f
1
 
 
 
k1
0.1
 
 
 
k2
1.8
 
 
 
k5
2
 
 
 
k6
0.2
 
 
 
k7
0.38