Diffusion-induced instability in a coupled reactor system: 
Case of the Deng-Harrison model
Authors' Data: Housam Binous & Nasri Zakia
Department of Chemical Engineering
National Institute of Applied Sciences and Technology
Tunis, TUNISIA
Email: binoushousam@yahoo.com

Reference :
I. Lengyel and I. R. Epstein, Diffusion-induced instability in chemically reacting systems: Steady-state multiplicity, oscillation, and chaos, Chaos 1 (1) 69-76, 1991.

Bifurcation Diagram - Computation takes over one hour using a Pentium 3 800 MHz Computer. We get a similar result as Figure 10 in the article by Lengyel and Epstein.

a=8.951;b=11.0;q=0.5;Dx=10^-5;Dy=10^-3;

sol[c_]:=NDSolve[{b-x1[t]-x1[t] y1[t]/(1+q x1[t]^2)+Dx (10^c)(x2[t]-x1[t])==D[x1[t],{t,1}],
b-x2[t]-x2[t] y2[t]/(1+q x2[t]^2)-Dx (10^c)(x2[t]-x1[t])==D[x2[t],{t,1}],
a-x1[t] y1[t]/(1+q x1[t]^2)+Dy (10^c)(y2[t]-y1[t])==D[y1[t],{t,1}],
a-x2[t] y2[t]/(1+q x2[t]^2)-Dy (10^c) (y2[t]-y1[t])==D[y2[t],{t,1}],x1[0]== 0.5,x2[0]== 0.5,y1[0]== 1,y2[0]== 1},{x1[t],x2[t],y1[t],y2[t]},{t,0,10000},MaxSteps-> 1000000]

p=0;

While[p<401,{c=2.7+0.005*p,f=sol[c],p+=1,Print[c],i=0,k=0,While[i<801,{t0=1000+10*i,i+=1,solt[i]=Quiet[FindRoot[D[First[x2[t]/.f],{t,1}]==0,{t,t0}]],If[1000<(t/.solt[i])<9000 ,{pt[k]={c,First[x2[t]/.f/.solt[i]]},k+=1}]}],tbl[p]=Table[pt[i],{i,1,k-1}]}]

plt[i_]:=ListPlot[tbl[i],PlotRange-> All,AspectRatio->1,AxesOrigin->{2.7,0.8},Frame->True,PlotStyle-> {PointSize[0.0029],RGBColor[1,0,0]}]

Show[Table[plt[i],{i,1,400}]]