Polo kináz modell

Előkészítés: 3-as modellben a felírt egyenletek és a referencia-paraméterértékek:

Needs["PlotLegends`"]

valtozok={x[t],y[t],z[t],w[t]};

modeleq={x'[t]==k1-(k21+k22*w[t]+k23*(t1-y[t]))*x[t],
y'[t]==-(((k71+k72*x[t])*(t1-y[t]))/(j7+(t1-y[t])))+((k8*y[t])/(j8+y[t])),
z'[t]==-((k3*z[t])/(j3+z[t]))+(((k41+k42*x[t])*(t2-z[t]))/(j4+t2-z[t])),
w'[t]==-(((k61+k62*x[t]) *w[t])/(j6 + w[t]))+(((k51 + k52*z[t])*(t3-w[t]))/(j5 + t3-w[t]))};

inipar={x[0]==1,y[0]==1,z[0]==1,w[0]==1};

params={k1,k21,k22,k23,k3,k41,k42,k51,k52,k61,k62,k71,k72,k8, t3,t1,t2,j3,j4,j5,j6,j7,j8} ;

refparam={k1->0.35, k21->5.5, k22->0.7, k23->1, k3->1.8, k41->0.0001, k42->0.7, k51->0.001, k52->2.2, k61->0.005, k62->2.2, k71->0.001, k72->0.8, k8->4.4,t1->0.2,t2->1.3,t3->2.5,j3->0.002, j4->0.01,j5->0.01, j6->0.7, j7->0.01,j8->0.01};

nds=NDSolve[Join[modeleq,inipar]/.refparam,{x[t],y[t],z[t],w[t]},{t,0,500},MaxSteps->100000];

plot1=Plot[{x[t]/.nds,y[t]/.nds,z[t]/.nds,w[t]/.nds},{t,0,20},PlotStyle->{Red,Blue,Black,Green}, PlotLegend->{"x(t)","y(t)","z(t)","w(t)"},LegendPosition->{1,-0.5},ImageSize->400]

FindMinimum[x[t]/.nds,{t,8}]

FindMinimum[x[t]/.nds,{t,12}]

tau=11.5945-8.1265

A nyers érzékenység:

J[t]=D[#,{valtozok}]&/@modeleq[[All,2]];

lista1=First/@refparam

lista2=Transpose[{{xk1[t],yk1[t],zk1[t],wk1[t]},{xk21[t],yk21[t],zk21[t],wk21[t]},{xk22[t],yk22[t],zk22[t],wk22[t]},{xk23[t],yk23[t],zk23[t],wk23[t]},{xk3[t],yk3[t],zk3[t],wk3[t]},{xk41[t],yk41[t],zk41[t],wk41[t]},{xk42[t],yk42[t],zk42[t],wk42[t]},{xk51[t],yk51[t],zk51[t],wk51[t]},{xk52[t],yk52[t],zk52[t],wk52[t]},{xk61[t],yk61[t],zk61[t],wk61[t]},{xk62[t],yk62[t],zk62[t],wk62[t]},{xk71[t],yk71[t],zk71[t],wk71[t]},{xk72[t],yk72[t],zk72[t],wk72[t]},{xk8[t],yk8[t],zk8[t],wk8[t]},{xt1[t],yt1[t],zt1[t],wt1[t]},{xt2[t],yt2[t],zt2[t],wt2[t]},{xt3[t],yt3[t],zt3[t],wt3[t]},{xj3[t],yj3[t],zj3[t],wj3[t]},{xj4[t],yj4[t],zj4[t],wj4[t]},{xj5[t],yj5[t],zj5[t],wj5[t]},{xj6[t],yj6[t],zj6[t],wj6[t]},{xj7[t],yj7[t],zj7[t],wj7[t]},{xj8[t],yj8[t],zj8[t],wj8[t]}}];

Sjobbo[t]=J[t].lista2+Transpose[Map[{D[modeleq[[All,2]][[1]],lista1[[#]]],D[modeleq[[All,2]][[2]],lista1[[#]]],D[modeleq[[All,2]][[3]],lista1[[#]]],D[modeleq[[All,2]][[4]],lista1[[#]]]}&,Range[23]]];

Sbalo[t]=Transpose[{{xk1'[t],yk1'[t],zk1'[t],wk1'[t]},{xk21'[t],yk21'[t],zk21'[t],wk21'[t]},{xk22'[t],yk22'[t],zk22'[t],wk22'[t]},{xk23'[t],yk23'[t],zk23'[t],wk23'[t]},{xk3'[t],yk3'[t],zk3'[t],wk3'[t]},{xk41'[t],yk41'[t],zk41'[t],wk41'[t]},{xk42'[t],yk42'[t],zk42'[t],wk42'[t]},{xk51'[t],yk51'[t],zk51'[t],wk51'[t]},{xk52'[t],yk52'[t],zk52'[t],wk52'[t]},{xk61'[t],yk61'[t],zk61'[t],wk61'[t]},{xk62'[t],yk62'[t],zk62'[t],wk62'[t]},{xk71'[t],yk71'[t],zk71'[t],wk71'[t]},{xk72'[t],yk72'[t],zk72'[t],wk72'[t]},{xk8'[t],yk8'[t],zk8'[t],wk8'[t]},{xt1'[t],yt1'[t],zt1'[t],wt1'[t]},{xt2'[t],yt2'[t],zt2'[t],wt2'[t]},{xt3'[t],yt3'[t],zt3'[t],wt3'[t]},{xj3'[t],yj3'[t],zj3'[t],wj3'[t]},{xj4'[t],yj4'[t],zj4'[t],wj4'[t]},{xj5'[t],yj5'[t],zj5'[t],wj5'[t]},{xj6'[t],yj6'[t],zj6'[t],wj6'[t]},{xj7'[t],yj7'[t],zj7'[t],wj7'[t]},{xj8'[t],yj8'[t],zj8'[t],wj8'[t]}}];

erzekeny=Map[Thread[Sjobbo[t][[#]]==Sbalo[t][[#]]]&,Range[4]];

inierzekeny={xk1[0]==0,yk1[0]==0,zk1[0]==0,wk1[0]==0,xk21[0]==0,yk21[0]==0,zk21[0]==0,wk21[0]==0,xk22[0]==0,yk22[0]==0,zk22[0]==0,wk22[0]==0,xk23[0]==0,yk23[0]==0,zk23[0]==0,wk23[0]==0,xk3[0]==0,yk3[0]==0,zk3[0]==0,wk3[0]==0,xk41[0]==0,yk41[0]==0,zk41[0]==0,wk41[0]==0,xk42[0]==0,yk42[0]==0,zk42[0]==0,wk42[0]==0,xk51[0]==0,yk51[0]==0,zk51[0]==0,wk51[0]==0,xk52[0]==0,yk52[0]==0,zk52[0]==0,wk52[0]==0,xk61[0]==0,yk61[0]==0,zk61[0]==0,wk61[0]==0,xk62[0]==0,yk62[0]==0,zk62[0]==0,wk62[0]==0,xk71[0]==0,yk71[0]==0,zk71[0]==0,wk71[0]==0,xk72[0]==0,yk72[0]==0,zk72[0]==0,wk72[0]==0,xk8[0]==0,yk8[0]==0,zk8[0]==0,wk8[0]==0,xt1[0]==0,yt1[0]==0,zt1[0]==0,wt1[0]==0,xt2[0]==0,yt2[0]==0,zt2[0]==0,wt2[0]==0,xt3[0]==0,yt3[0]==0,zt3[0]==0,wt3[0]==0,xj3[0]==0,yj3[0]==0,zj3[0]==0,wj3[0]==0,xj4[0]==0,yj4[0]==0,zj4[0]==0,wj4[0]==0,xj5[0]==0,yj5[0]==0,zj5[0]==0,wj5[0]==0,xj6[0]==0,yj6[0]==0,zj6[0]==0,wj6[0]==0,xj7[0]==0,yj7[0]==0,zj7[0]==0,wj7[0]==0,xj8[0]==0,yj8[0]==0,zj8[0]==0,wj8[0]==0};

mo=NDSolve[Join[modeleq,inipar,erzekeny,inierzekeny]/.refparam,{x[t],y[t],z[t],w[t],xk1[t],yk1[t],zk1[t],wk1[t],xk21[t],yk21[t],zk21[t],wk21[t],xk22[t],yk22[t],zk22[t],wk22[t],xk23[t],yk23[t],zk23[t],wk23[t],xk3[t],yk3[t],zk3[t],wk3[t],xk41[t],yk41[t],zk41[t],wk41[t],xk42[t],yk42[t],zk42[t],wk42[t],xk51[t],yk51[t],zk51[t],wk51[t],xk52[t],yk52[t],zk52[t],wk52[t],xk61[t],yk61[t],zk61[t],wk61[t],xk62[t],yk62[t],zk62[t],wk62[t],xk71[t],yk71[t],zk71[t],wk71[t],xk72[t],yk72[t],zk72[t],wk72[t],xk8[t],yk8[t],zk8[t],wk8[t],xt1[t],yt1[t],zt1[t],wt1[t],xt2[t],yt2[t],zt2[t],wt2[t],xt3[t],yt3[t],zt3[t],wt3[t],xj3[t],yj3[t],zj3[t],wj3[t],xj4[t],yj4[t],zj4[t],wj4[t],xj5[t],yj5[t],zj5[t],wj5[t],xj6[t],yj6[t],zj6[t],wj6[t],xj7[t],yj7[t],zj7[t],wj7[t],xj8[t],yj8[t],zj8[t],wj8[t]},{t,0,100},MaxSteps->100000];

A nyers ézrékenységek:

GraphicsArray[Table[Plot[lista2[[i,j]]/.mo/.refparam,{t,0,30},PlotLabel->{valtozok[[i]],lista1[[j]]}],{j,23},{i,4}]]

Periódusérzékenység :

S1[t]={{xk1[t],xk21[t],xk22[t],xk23[t],xk3[t],xk41[t],xk42[t],xk51[t],xk52[t],xk61[t],xk62[t],xk71[t],xk72[t],xk8[t], xt1[t],xt2[t],xt3[t],xj3[t],xj4[t],xj5[t],xj6[t],xj7[t],xj8[t]},{yk1[t],yk21[t],yk22[t],yk23[t],yk3[t],yk41[t],yk42[t],yk51[t],yk52[t],yk61[t],yk62[t],yk71[t],yk72[t],yk8[t],yt1[t],yt2[t],yt3[t],yj3[t],yj4[t],yj5[t],yj6[t],yj7[t],yj8[t]},{zk1[t],zk21[t],zk22[t],zk23[t],zk3[t],zk41[t],zk42[t],zk51[t],zk52[t],zk61[t],zk62[t],zk71[t],zk72[t],zk8[t],zt1[t],zt2[t], zt3[t],zj3[t],zj4[t],zj5[t],zj6[t],zj7[t],zj8[t]},{wk1[t],wk21[t],wk22[t],wk23[t],wk3[t],wk41[t],wk42[t],wk51[t],wk52[t],wk61[t],wk62[t],wk71[t],wk72[t],wk8[t], wt1[t],wt2[t],wt3[t],wj3[t],wj4[t],wj5[t],wj6[t],wj7[t],wj8[t]}}/.mo;

S1=S1[t]/.t->45;

SingularValueDecomposition[S1];

v={SingularValueDecomposition[S1]}[[1,3,1]]

sigma={SingularValueDecomposition[S1]}[[1,2,1,1]]

norma=Norm[modeleq[[All,2]]]/.refparam/.mo;

S1tau=tau*sigma/norma[[1]]/t*v;

Plot[Evaluate[S1tau[[1]]],{t,0,45}]

Normált periódusérzékenységek :

GraphicsArray[Table[Plot[S1tau[[i]]*i/tau/.mo/.refparam,{t,0,45},PlotLabel->{i}],{i,23}]]

Másik megoldás a periódusérzékenységek (Sτ) kiszámítására:

motnelkul=NDSolve[Join[modeleq,inipar,erzekeny,inierzekeny]/.refparam,{x,y,z,w,xk1,yk1,zk1,wk1,xk21,yk21,zk21,wk21,xk22,yk22,zk22,wk22,xk23,yk23,zk23,wk23,xk3,yk3,zk3,wk3,xk41,yk41,zk41,wk41,xk42,yk42,zk42,wk42,xk51,yk51,zk51,wk51,xk52,yk52,zk52,wk52,xk61,yk61,zk61,wk61,xk62,yk62,zk62,wk62,xk71,yk71,zk71,wk71,xk72,yk72,zk72,wk72,xk8,yk8,zk8,wk8,xt1,yt1,zt1,wt1,xt2,yt2,zt2,wt2,xt3,yt3,zt3,wt3,xj3,yj3,zj3,wj3,xj4,yj4,zj4,wj4,xj5,yj5,zj5,wj5,xj6,yj6,zj6,wj6,xj7,yj7,zj7,wj7,xj8,yj8,zj8,wj8},{t,0,100},MaxSteps->100000];

lista2tnelkul=lista2/.{xx_[t]->xx}

S1:=(lista2tnelkul[[1]]/.motnelkul)[[1]]

szaml[t_]:=Through[S1[t]]-Through[S1[t+tau]]

nev[t_]:=modeleq[[1,2]]/.refparam/.nds

konst[i_][t_]:=szaml[t][[i]]/nev[t]

kozel[i_][delta_]:=Table[konst[i][t][[1]],{t,70,70+3*3.468,delta}]

int[i_][delta_,k_]:=Integrate[Interpolation[kozel[i][delta],InterpolationOrder->k][x],{x,70,70+3*3.468}]

Timing[TableForm[Table[int[1][delta,3],{delta,0.00001,0.00010,0.00001}],TableHeadings->{Range[0.00001,0.00010,0.00001],None}]]

stau[1]=-74.57073782779244`/(3*3.468)

Timing[TableForm[Table[int[2][delta,3],{delta,0.00001,0.00010,0.00001}],TableHeadings->{Range[0.00001,0.00010,0.00001],None}]]

stau[2]=0.24105434231102105`/(3*3.468)

TableForm[Table[int[3][delta,3],{delta,0.00001,0.00010,0.00001}],TableHeadings->{Range[0.00001,0.00010,0.00001],None}]

stau[3]=33.99028842703933`/(3*3.468)

TableForm[Table[int[4][delta,3],{delta,0.00001,0.00010,0.00001}],TableHeadings->{Range[0.00001,0.00010,0.00001],None}]

stau[4]=-105.68496957137492`/(3*3.468)

TableForm[Table[int[5][delta,3],{delta,0.00001,0.00010,0.00001}],TableHeadings->{Range[0.00001,0.00010,0.00001],None}]

stau[5]=-24.423261743205877`/(3*3.468)

TableForm[Table[int[6][delta,3],{delta,0.00001,0.00010,0.00001}],TableHeadings->{Range[0.00001,0.00010,0.00001],None}]

stau[6]=22.824228756098766`/(3*3.468)

TableForm[Table[int[7][delta,3],{delta,0.00001,0.00010,0.00001}],TableHeadings->{Range[0.00001,0.00010,0.00001],None}]

stau[7]=27.21325585937739`/(3*3.468)

TableForm[Table[int[8][delta,3],{delta,0.00001,0.00010,0.00001}],TableHeadings->{Range[0.00001,0.00010,0.00001],None}]

stau[8]=31.670740156250222`/(3*3.468)

TableForm[Table[int[9][delta,3],{delta,0.00001,0.00010,0.00001}],TableHeadings->{Range[0.00001,0.00010,0.00001],None}]

stau[9]=16.423082207401087`/(3*3.468)

TableForm[Table[int[10][delta,3],{delta,0.00001,0.00010,0.00001}],TableHeadings->{Range[0.00001,0.00010,0.00001],None}]

stau[10]=-16.72582094153103`/(3*3.468)

TableForm[Table[int[11][delta,3],{delta,0.00001,0.00010,0.00001}],TableHeadings->{Range[0.00001,0.00010,0.00001],None}]

stau[11]=-12.025006293759361`/(3*3.468)

TableForm[Table[int[12][delta,3],{delta,0.00001,0.00010,0.00001}],TableHeadings->{Range[0.00001,0.00010,0.00001],None}]

stau[12]=20.216757679842267`/(3*3.468)

TableForm[Table[int[13][delta,3],{delta,0.00001,0.00010,0.00001}],TableHeadings->{Range[0.00001,0.00010,0.00001],None}]

stau[13]=-22.596010693633485`/(3*3.468)

TableForm[Table[int[14][delta,3],{delta,0.00001,0.00010,0.00001}],TableHeadings->{Range[0.00001,0.00010,0.00001],None}]

stau[14]=-19.971086462048888`/(3*3.468)

TableForm[Table[int[15][delta,3],{delta,0.00001,0.00010,0.00001}],TableHeadings->{Range[0.00001,0.00010,0.00001],None}]

stau[15]=0.46349874012009584`/(3*3.468)

TableForm[Table[int[16][delta,3],{delta,0.00001,0.00010,0.00001}],TableHeadings->{Range[0.00001,0.00010,0.00001],None}]

stau[16]=47.54550459025057`/(3*3.468)

TableForm[Table[int[17][delta,3],{delta,0.00001,0.00010,0.00001}],TableHeadings->{Range[0.00001,0.00010,0.00001],None}]

stau[17]=0.11658268988347899`/(3*3.468)

TableForm[Table[int[18][delta,3],{delta,0.00001,0.00010,0.00001}],TableHeadings->{Range[0.00001,0.00010,0.00001],None}]

stau[18]=68.2680185717047`/(3*3.468)

TableForm[Table[int[19][delta,3],{delta,0.00001,0.00010,0.00001}],TableHeadings->{Range[0.00001,0.00010,0.00001],None}]

stau[19]=-199.6471393298466`/(3*3.468)

TableForm[Table[int[20][delta,3],{delta,0.00001,0.00010,0.00001}],TableHeadings->{Range[0.00001,0.00010,0.00001],None}]

stau[20]=-20.276244164818664`/(3*3.468)

TableForm[Table[int[21][delta,3],{delta,0.00001,0.00010,0.00001}],TableHeadings->{Range[0.00001,0.00010,0.00001],None}]

stau[21]=19.04312098758612`/(3*3.468)

TableForm[Table[int[22][delta,3],{delta,0.00001,0.00010,0.00001}],TableHeadings->{Range[0.00001,0.00010,0.00001],None}]

stau[22]=33.71492350314593`/(3*3.468)

TableForm[Table[int[23][delta,3],{delta,0.00001,0.00010,0.00001}],TableHeadings->{Range[0.00001,0.00010,0.00001],None}]

stau[23]=50.98064933731287`/(3*3.468)

A tisztított érzékenységek

GraphicsArray[Partition[Table[Plot[Evaluate[(lista2[[1,j]]+t/tau*stau[j]*(k1-(k21+k22*w[t]+k23*(t1-y[t]))*x[t])/.refparam/.nds/.mo)],{t,0,30},PlotLabel->{valtozok[[1]],lista1[[j]]}],{j,23}],4,4,1,{}]]

GraphicsArray[Partition[Table[Plot[Evaluate[(lista2[[2,j]]+t/tau*stau[j]*(-(((k71+k72*x[t])*(t1-y[t]))/(j7+(t1-y[t])))+((k8*y[t])/(j8+y[t])))/.refparam/.nds/.mo)],{t,0,30},PlotLabel->{valtozok[[2]],lista1[[j]]}],{j,23}],4,4,1,{}]]

GraphicsArray[Partition[Table[Plot[Evaluate[(lista2[[3,j]]+t/tau*stau[j]*(-((k3*z[t])/(j3+z[t]))+(((k41+k42*x[t])*(t2-z[t]))/(j4+t2-z[t])))/.refparam/.nds/.mo)],{t,0,30},PlotLabel->{valtozok[[3]],lista1[[j]]}],{j,23}],4,4,1,{}]]

GraphicsArray[Partition[Table[Plot[Evaluate[(lista2[[4,j]]+t/tau*stau[j]*(-(((k61+k62*x[t]) *w[t])/(j6 + w[t]))+(((k51 + k52*z[t])*(t3-w[t]))/(j5 + t3-w[t])))/.refparam/.nds/.mo)],{t,0,30},PlotLabel->{valtozok[[4]],lista1[[j]]}],{j,23}],4,4,1,{}]]

Korrigált periódusérzékenységek

stau[1]=-74.57073782779244`/(3*3.468)

staukoz[1]=-1.15770651939566`

Plot[Evaluate[(xk1[t]+t/tau*staukoz[1]*(k1-(k21+k22*w[t]+k23*(t1-y[t]))*x[t])/.refparam/.nds/.mo)],{t,0,100},PlotRange->All]

staukoz[2]=-0.07405434231102105`/(3*3.468)

staukoz[3]=0.548

staukoz[4]=-1.575

staukoz[5]=-0.404

staukoz[6]=0.376

staukoz[7]=0.4556

staukoz[8]=0.501

staukoz[9]=0.271

staukoz[10]=-0.2615

staukoz[11]=-0.1982

staukoz[12]=0.2993

staukoz[13]=-0.36

staukoz[14]=-0.295

staukoz[15]=0.00189

staukoz[16]=-0.0038

staukoz[17]=0.795

staukoz[18]=1.115

staukoz[19]=-3.350

staukoz[20]=-0.334

staukoz[21]=0.317

staukoz[22]=0.54

staukoz[23]=0.787

Korrigált tisztított preriódusérzékenységek

GraphicsArray[Partition[Table[Plot[Evaluate[(lista2[[1,j]]+t/tau*staukoz[j]*(k1-(k21+k22*w[t]+k23*(t1-y[t]))*x[t])/.refparam/.nds/.mo)],{t,0,60},PlotLabel->{valtozok[[1]],lista1[[j]]}],{j,23}],4,4,1,{}]]

GraphicsArray[Partition[Table[Plot[Evaluate[(lista2[[2,j]]+t/tau*staukoz[j]*(-(((k71+k72*x[t])*(t1-y[t]))/(j7+(t1-y[t])))+((k8*y[t])/(j8+y[t])))/.refparam/.nds/.mo)],{t,0,60},PlotLabel->{valtozok[[2]],lista1[[j]]}],{j,23}],4,4,1,{}]]

GraphicsArray[Partition[Table[Plot[Evaluate[(lista2[[3,j]]+t/tau*staukoz[j]*(-((k3*z[t])/(j3+z[t]))+(((k41+k42*x[t])*(t2-z[t]))/(j4+t2-z[t])))/.refparam/.nds/.mo)],{t,0,60},PlotLabel->{valtozok[[3]],lista1[[j]]}],{j,23}],4,4,1,{}]]

GraphicsArray[Partition[Table[Plot[Evaluate[(lista2[[4,j]]+t/tau*staukoz[j]*(-(((k61+k62*x[t]) *w[t])/(j6 + w[t]))+(((k51 + k52*z[t])*(t3-w[t]))/(j5 + t3-w[t])))/.refparam/.nds/.mo)],{t,0,60},PlotLabel->{valtozok[[4]],lista1[[j]]}],{j,23}],4,4,1,{}]]

Normált korrigált tisztított érzékenységek

GraphicsArray[Partition[Table[Plot[Evaluate[((lista2[[1,j]]+t/tau*staukoz[j]*(k1-(k21+k22*w[t]+k23*(t1-y[t]))*x[t]))/x[t]/.refparam/.nds/.mo)],{t,0,60},PlotLabel->{valtozok[[1]],lista1[[j]]}],{j,23}],4,4,1,{}]]

GraphicsArray[Partition[Table[Plot[Evaluate[((lista2[[2,j]]+t/tau*staukoz[j]*(-(((k71+k72*x[t])*(t1-y[t]))/(j7+(t1-y[t])))+((k8*y[t])/(j8+y[t]))))/y[t]/.refparam/.nds/.mo)],{t,0,60},PlotLabel->{valtozok[[2]],lista1[[j]]}],{j,23}],4,4,1,{}]]

GraphicsArray[Partition[Table[Plot[Evaluate[((lista2[[3,j]]+t/tau*staukoz[j]*(-((k3*z[t])/(j3+z[t]))+(((k41+k42*x[t])*(t2-z[t]))/(j4+t2-z[t]))))/z[t]/.refparam/.nds/.mo)],{t,0,60},PlotLabel->{valtozok[[3]],lista1[[j]]}],{j,23}],4,4,1,{}]]

GraphicsArray[Partition[Table[Plot[Evaluate[((lista2[[4,j]]+t/tau*staukoz[j]*(-(((k61+k62*x[t]) *w[t])/(j6 + w[t]))+(((k51 + k52*z[t])*(t3-w[t]))/(j5 + t3-w[t]))))/w[t]/.refparam/.nds/.mo)],{t,0,60},PlotLabel->{valtozok[[4]],lista1[[j]]}],{j,23}],4,4,1,{}]]

Integrálközepek :

vektorx[i_][t_]:=(lista2[[1,i]]+t/tau*staukoz[i]*(k1-(k21+k22*w[t]+k23*(t1-y[t]))*x[t]))/x[t]/.refparam/.nds/.mo

vektory[i_][t_]:=(lista2[[2,i]]+t/tau*staukoz[i]*(-(((k71+k72*x[t])*(t1-y[t]))/(j7+(t1-y[t])))+((k8*y[t])/(j8+y[t]))))/y[t]/.refparam/.nds/.mo

vektorz[i_][t_]:=(lista2[[3,i]]+t/tau*staukoz[i]*(-((k3*z[t])/(j3+z[t]))+(((k41+k42*x[t])*(t2-z[t]))/(j4+t2-z[t]))))/z[t]/.refparam/.nds/.mo

vektorw[i_][t_]:=(lista2[[4,i]]+t/tau*staukoz[i]*(-(((k61+k62*x[t]) *w[t])/(j6 + w[t]))+(((k51 + k52*z[t])*(t3-w[t]))/(j5 + t3-w[t]))))/w[t]/.refparam/.nds/.mo

kozelx[i_][delta_]:=Table[vektorx[i][t][[1]],{t,60,60+2*tau,delta}]

integralx[i_][delta_,k_]:=Integrate[Interpolation[kozelx[i][delta],InterpolationOrder->k][x],{x,60,60+2*tau}]

kozely[i_][delta_]:=Table[vektory[i][t][[1]],{t,60,60+2*tau,delta}]

integraly[i_][delta_,k_]:=Integrate[Interpolation[kozely[i][delta],InterpolationOrder->k][x],{x,60,60+2*tau}]

kozelz[i_][delta_]:=Table[vektorz[i][t][[1]],{t,60,60+2*tau,delta}]

integralz[i_][delta_,k_]:=Integrate[Interpolation[kozelz[i][delta],InterpolationOrder->k][x],{x,60,60+2*tau}]

kozelw[i_][delta_]:=Table[vektorw[i][t][[1]],{t,60,60+2*tau,delta}]

integralw[i_][delta_,k_]:=Integrate[Interpolation[kozelw[i][delta],InterpolationOrder->k][x],{x,60,60+2*tau}]

listax=Map[integralx[#][0.0001,3]&,Range[23]]

listay=Map[integraly[#][0.0001,3]&,Range[23]]

listaz=Map[integralz[#][0.0001,3]&,Range[23]]

listaw=Map[integralw[#][0.0001,3]&,Range[23]]

Az integrálközepek rendre :

lista=Join[listax,listay,listaz,listaw]/(2tau)

Az érzékenységi vektor hossza :

Norm[lista]